LMFDB - Embedded newform 13.11.d.a.5.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,11,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.25964428476$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 18 x^{18} + 32284 x^{17} + 16288321 x^{16} - 1399914 x^{15} + 236338034 x^{14} + \cdots + 84\!\cdots\!04 $ x^20 - 6x^19 + 18x^18 + 32284x^17 + 16288321x^16 - 1399914x^15 + 236338034x^14 + 223248859576x^13 + 68334664655952x^12 + 197812095245952x^11 + 941899764571520x^10 + 335247771330255360x^9 + 58398135128630811648x^8 + 300750323152050266112x^7 + 1118531393884122341376x^6 + 105977196796457311174656x^5 + 10666527336316281117671424x^4 + 85502397039865581748617216x^3 + 318723107626870315852234752x^2 - 2323063126834144103834320896*x + 8466004130416338670089928704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{6}\cdot 13^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.3
Root			$-20.7752 - 20.7752i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.11.d.a.8.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-22.7752 + 22.7752i) q^{2} +85.0537 q^{3} -13.4171i q^{4} +(-1400.68 + 1400.68i) q^{5} +(-1937.11 + 1937.11i) q^{6} +(17603.1 + 17603.1i) q^{7} +(-23016.2 - 23016.2i) q^{8} -51814.9 q^{9} -63801.5i q^{10} +(-156027. - 156027. i) q^{11} -1141.18i q^{12} +(-94245.1 - 359133. i) q^{13} -801827. q^{14} +(-119133. + 119133. i) q^{15} +1.06214e6 q^{16} +1.06393e6i q^{17} +(1.18009e6 - 1.18009e6i) q^{18} +(-2.58474e6 + 2.58474e6i) q^{19} +(18793.1 + 18793.1i) q^{20} +(1.49721e6 + 1.49721e6i) q^{21} +7.10710e6 q^{22} -7.02548e6i q^{23} +(-1.95761e6 - 1.95761e6i) q^{24} +5.84181e6i q^{25} +(1.03258e7 + 6.03286e6i) q^{26} -9.42938e6 q^{27} +(236183. - 236183. i) q^{28} +1.57742e7 q^{29} -5.42655e6i q^{30} +(-2.05535e7 + 2.05535e7i) q^{31} +(-621723. + 621723. i) q^{32} +(-1.32707e7 - 1.32707e7i) q^{33} +(-2.42312e7 - 2.42312e7i) q^{34} -4.93126e7 q^{35} +695207. i q^{36} +(3.47845e7 + 3.47845e7i) q^{37} -1.17736e8i q^{38} +(-8.01589e6 - 3.05456e7i) q^{39} +6.44767e7 q^{40} +(-7.78807e7 + 7.78807e7i) q^{41} -6.81983e7 q^{42} -6.47108e7i q^{43} +(-2.09344e6 + 2.09344e6i) q^{44} +(7.25761e7 - 7.25761e7i) q^{45} +(1.60007e8 + 1.60007e8i) q^{46} +(2.50965e8 + 2.50965e8i) q^{47} +9.03385e7 q^{48} +3.37262e8i q^{49} +(-1.33048e8 - 1.33048e8i) q^{50} +9.04911e7i q^{51} +(-4.81853e6 + 1.26450e6i) q^{52} -2.12568e8 q^{53} +(2.14756e8 - 2.14756e8i) q^{54} +4.37089e8 q^{55} -8.10312e8i q^{56} +(-2.19842e8 + 2.19842e8i) q^{57} +(-3.59260e8 + 3.59260e8i) q^{58} +(-3.79263e8 - 3.79263e8i) q^{59} +(1.59842e6 + 1.59842e6i) q^{60} -7.59120e8 q^{61} -9.36221e8i q^{62} +(-9.12102e8 - 9.12102e8i) q^{63} +1.05931e9i q^{64} +(6.35038e8 + 3.71023e8i) q^{65} +6.04485e8 q^{66} +(-6.35699e8 + 6.35699e8i) q^{67} +1.42749e7 q^{68} -5.97543e8i q^{69} +(1.12310e9 - 1.12310e9i) q^{70} +(-1.58458e9 + 1.58458e9i) q^{71} +(1.19258e9 + 1.19258e9i) q^{72} +(2.09826e9 + 2.09826e9i) q^{73} -1.58445e9 q^{74} +4.96868e8i q^{75} +(3.46798e7 + 3.46798e7i) q^{76} -5.49312e9i q^{77} +(8.78244e8 + 5.13117e8i) q^{78} +3.56842e9 q^{79} +(-1.48771e9 + 1.48771e9i) q^{80} +2.25761e9 q^{81} -3.54749e9i q^{82} +(-3.11216e9 + 3.11216e9i) q^{83} +(2.00882e7 - 2.00882e7i) q^{84} +(-1.49022e9 - 1.49022e9i) q^{85} +(1.47380e9 + 1.47380e9i) q^{86} +1.34165e9 q^{87} +7.18231e9i q^{88} +(5.13947e7 + 5.13947e7i) q^{89} +3.30587e9i q^{90} +(4.66284e9 - 7.98085e9i) q^{91} -9.42618e7 q^{92} +(-1.74816e9 + 1.74816e9i) q^{93} -1.14315e10 q^{94} -7.24079e9i q^{95} +(-5.28798e7 + 5.28798e7i) q^{96} +(-5.12170e9 + 5.12170e9i) q^{97} +(-7.68120e9 - 7.68120e9i) q^{98} +(8.08453e9 + 8.08453e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) $ 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−22.7752	+	22.7752i	−0.711724	+	0.711724i	−0.966896	−	0.255172i	$-0.917868\pi$
$2$	−22.7752	+	22.7752i	−0.711724	+	0.711724i	0.255172	+	0.966896i	$0.417868\pi$
$3$	85.0537			0.350015			0.175008	−	0.984567i	$-0.444005\pi$
$3$	85.0537			0.350015			0.175008	+	0.984567i	$0.444005\pi$
$4$		−	13.4171i		−	0.0131027i
$5$	−1400.68	+	1400.68i	−0.448218	+	0.448218i	−0.894762	−	0.446544i	$-0.852655\pi$
$5$	−1400.68	+	1400.68i	−0.448218	+	0.448218i	0.446544	+	0.894762i	$0.352655\pi$
$6$	−1937.11	+	1937.11i	−0.249114	+	0.249114i
$7$	17603.1	+	17603.1i	1.04737	+	1.04737i	0.998821	+	0.0485454i	$0.0154585\pi$
$7$	17603.1	+	17603.1i	1.04737	+	1.04737i	0.0485454	+	0.998821i	$0.484541\pi$
$8$	−23016.2	−	23016.2i	−0.702399	−	0.702399i
$9$	−51814.9			−0.877489
$10$		−	63801.5i		−	0.638015i
$11$	−156027.	−	156027.i	−0.968807	−	0.968807i	0.0307214	−	0.999528i	$-0.490220\pi$
$11$	−156027.	−	156027.i	−0.968807	−	0.968807i	−0.999528	+	0.0307214i	$0.990220\pi$
$12$		−	1141.18i		−	0.00458613i
$13$	−94245.1	−	359133.i	−0.253829	−	0.967249i
$13$	−94245.1	−	359133.i	−0.253829	−	0.967249i
$14$	−801827.			−1.49087
$15$	−119133.	+	119133.i	−0.156883	+	0.156883i
$16$	1.06214e6			1.01293
$17$			1.06393e6i			0.749321i	0.927162	+	0.374660i	$0.122241\pi$
$17$			1.06393e6i			0.749321i	−0.927162	+	0.374660i	$0.877759\pi$
$18$	1.18009e6	−	1.18009e6i	0.624530	−	0.624530i
$19$	−2.58474e6	+	2.58474e6i	−1.04388	+	1.04388i	−0.0448839	+	0.998992i	$0.514292\pi$
$19$	−2.58474e6	+	2.58474e6i	−1.04388	+	1.04388i	−0.998992	+	0.0448839i	$0.985708\pi$
$20$	18793.1	+	18793.1i	0.00587285	+	0.00587285i
$21$	1.49721e6	+	1.49721e6i	0.366594	+	0.366594i
$22$	7.10710e6			1.37905
$23$		−	7.02548e6i		−	1.09153i	−0.837937	−	0.545767i	$-0.816239\pi$
$23$		−	7.02548e6i		−	1.09153i	0.837937	−	0.545767i	$-0.183761\pi$
$24$	−1.95761e6	−	1.95761e6i	−0.245850	−	0.245850i
$25$			5.84181e6i			0.598202i
$26$	1.03258e7	+	6.03286e6i	0.869071	+	0.507758i
$27$	−9.42938e6			−0.657150
$28$	236183.	−	236183.i	0.0137233	−	0.0137233i
$29$	1.57742e7			0.769055			0.384527	−	0.923114i	$-0.374364\pi$
$29$	1.57742e7			0.769055			0.384527	+	0.923114i	$0.374364\pi$
$30$		−	5.42655e6i		−	0.223315i
$31$	−2.05535e7	+	2.05535e7i	−0.717924	+	0.717924i	−0.968180	−	0.250256i	$-0.919485\pi$
$31$	−2.05535e7	+	2.05535e7i	−0.717924	+	0.717924i	0.250256	+	0.968180i	$0.419485\pi$
$32$	−621723.	+	621723.i	−0.0185288	+	0.0185288i
$33$	−1.32707e7	−	1.32707e7i	−0.339097	−	0.339097i
$34$	−2.42312e7	−	2.42312e7i	−0.533310	−	0.533310i
$35$	−4.93126e7			−0.938896
$36$			695207.i			0.0114975i
$37$	3.47845e7	+	3.47845e7i	0.501623	+	0.501623i	0.911942	−	0.410319i	$-0.134583\pi$
$37$	3.47845e7	+	3.47845e7i	0.501623	+	0.501623i	−0.410319	+	0.911942i	$0.634583\pi$
$38$		−	1.17736e8i		−	1.48590i
$39$	−8.01589e6	−	3.05456e7i	−0.0888441	−	0.338552i
$40$	6.44767e7			0.629655
$41$	−7.78807e7	+	7.78807e7i	−0.672219	+	0.672219i	−0.958227	−	0.286009i	$-0.907671\pi$
$41$	−7.78807e7	+	7.78807e7i	−0.672219	+	0.672219i	0.286009	+	0.958227i	$0.407671\pi$
$42$	−6.81983e7			−0.521828
$43$		−	6.47108e7i		−	0.440184i	−0.975479	−	0.220092i	$-0.929364\pi$
$43$		−	6.47108e7i		−	0.440184i	0.975479	−	0.220092i	$-0.0706358\pi$
$44$	−2.09344e6	+	2.09344e6i	−0.0126940	+	0.0126940i
$45$	7.25761e7	−	7.25761e7i	0.393306	−	0.393306i
$46$	1.60007e8	+	1.60007e8i	0.776870	+	0.776870i
$47$	2.50965e8	+	2.50965e8i	1.09427	+	1.09427i	0.995067	+	0.0992007i	$0.0316286\pi$
$47$	2.50965e8	+	2.50965e8i	1.09427	+	1.09427i	0.0992007	+	0.995067i	$0.468371\pi$
$48$	9.03385e7			0.354541
$49$			3.37262e8i			1.19395i
$50$	−1.33048e8	−	1.33048e8i	−0.425755	−	0.425755i
$51$			9.04911e7i			0.262274i
$52$	−4.81853e6	+	1.26450e6i	−0.0126735	+	0.00332584i
$53$	−2.12568e8			−0.508297			−0.254149	−	0.967165i	$-0.581795\pi$
$53$	−2.12568e8			−0.508297			−0.254149	+	0.967165i	$0.581795\pi$
$54$	2.14756e8	−	2.14756e8i	0.467709	−	0.467709i
$55$	4.37089e8			0.868473
$56$		−	8.10312e8i		−	1.47134i
$57$	−2.19842e8	+	2.19842e8i	−0.365373	+	0.365373i
$58$	−3.59260e8	+	3.59260e8i	−0.547355	+	0.547355i
$59$	−3.79263e8	−	3.79263e8i	−0.530494	−	0.530494i	0.390225	−	0.920720i	$-0.372397\pi$
$59$	−3.79263e8	−	3.79263e8i	−0.530494	−	0.530494i	−0.920720	+	0.390225i	$0.872397\pi$
$60$	1.59842e6	+	1.59842e6i	0.00205559	+	0.00205559i
$61$	−7.59120e8			−0.898796			−0.449398	−	0.893332i	$-0.648361\pi$
$61$	−7.59120e8			−0.898796			−0.449398	+	0.893332i	$0.648361\pi$
$62$		−	9.36221e8i		−	1.02193i
$63$	−9.12102e8	−	9.12102e8i	−0.919053	−	0.919053i
$64$			1.05931e9i			0.986556i
$65$	6.35038e8	+	3.71023e8i	0.547309	+	0.319767i
$66$	6.04485e8			0.482687
$67$	−6.35699e8	+	6.35699e8i	−0.470845	+	0.470845i	−0.902188	−	0.431343i	$-0.858040\pi$
$67$	−6.35699e8	+	6.35699e8i	−0.470845	+	0.470845i	0.431343	+	0.902188i	$0.358040\pi$
$68$	1.42749e7			0.00981811
$69$		−	5.97543e8i		−	0.382053i
$70$	1.12310e9	−	1.12310e9i	0.668235	−	0.668235i
$71$	−1.58458e9	+	1.58458e9i	−0.878260	+	0.878260i	−0.993355	−	0.115094i	$-0.963283\pi$
$71$	−1.58458e9	+	1.58458e9i	−0.878260	+	0.878260i	0.115094	+	0.993355i	$0.463283\pi$
$72$	1.19258e9	+	1.19258e9i	0.616347	+	0.616347i
$73$	2.09826e9	+	2.09826e9i	1.01215	+	1.01215i	0.999925	+	0.0122232i	$0.00389087\pi$
$73$	2.09826e9	+	2.09826e9i	1.01215	+	1.01215i	0.0122232	+	0.999925i	$0.496109\pi$
$74$	−1.58445e9			−0.714035
$75$			4.96868e8i			0.209380i
$76$	3.46798e7	+	3.46798e7i	0.0136776	+	0.0136776i
$77$		−	5.49312e9i		−	2.02939i
$78$	8.78244e8	+	5.13117e8i	0.304188	+	0.177723i
$79$	3.56842e9			1.15969			0.579843	−	0.814728i	$-0.303114\pi$
$79$	3.56842e9			1.15969			0.579843	+	0.814728i	$0.303114\pi$
$80$	−1.48771e9	+	1.48771e9i	−0.454014	+	0.454014i
$81$	2.25761e9			0.647477
$82$		−	3.54749e9i		−	0.956868i
$83$	−3.11216e9	+	3.11216e9i	−0.790080	+	0.790080i	−0.981507	−	0.191427i	$-0.938688\pi$
$83$	−3.11216e9	+	3.11216e9i	−0.790080	+	0.790080i	0.191427	+	0.981507i	$0.438688\pi$
$84$	2.00882e7	−	2.00882e7i	0.00480336	−	0.00480336i
$85$	−1.49022e9	−	1.49022e9i	−0.335859	−	0.335859i
$86$	1.47380e9	+	1.47380e9i	0.313290	+	0.313290i
$87$	1.34165e9			0.269181
$88$			7.18231e9i			1.36098i
$89$	5.13947e7	+	5.13947e7i	0.00920382	+	0.00920382i	0.711694	−	0.702490i	$-0.247928\pi$
$89$	5.13947e7	+	5.13947e7i	0.00920382	+	0.00920382i	−0.702490	+	0.711694i	$0.747928\pi$
$90$			3.30587e9i			0.559851i
$91$	4.66284e9	−	7.98085e9i	0.747212	−	1.27892i
$92$	−9.42618e7			−0.0143020
$93$	−1.74816e9	+	1.74816e9i	−0.251284	+	0.251284i
$94$	−1.14315e10			−1.55763
$95$		−	7.24079e9i		−	0.935768i
$96$	−5.28798e7	+	5.28798e7i	−0.00648536	+	0.00648536i
$97$	−5.12170e9	+	5.12170e9i	−0.596424	+	0.596424i	−0.939359	−	0.342935i	$-0.888579\pi$
$97$	−5.12170e9	+	5.12170e9i	−0.596424	+	0.596424i	0.342935	+	0.939359i	$0.388579\pi$
$98$	−7.68120e9	−	7.68120e9i	−0.849765	−	0.849765i
$99$	8.08453e9	+	8.08453e9i	0.850117	+	0.850117i
$100$	7.83804e7			0.00783804
$101$		−	8.10844e9i		−	0.771490i	−0.922605	−	0.385745i	$-0.873944\pi$
$101$		−	8.10844e9i		−	0.771490i	0.922605	−	0.385745i	$-0.126056\pi$
$102$	−2.06095e9	−	2.06095e9i	−0.186667	−	0.186667i
$103$		−	1.21742e10i		−	1.05016i	−0.851054	−	0.525079i	$-0.824036\pi$
$103$		−	1.21742e10i		−	1.05016i	0.851054	−	0.525079i	$-0.175964\pi$
$104$	−6.09671e9	+	1.04350e10i	−0.501105	+	0.857684i
$105$	−4.19422e9			−0.328628
$106$	4.84126e9	−	4.84126e9i	0.361767	−	0.361767i
$107$	4.95855e9			0.353538			0.176769	−	0.984252i	$-0.443435\pi$
$107$	4.95855e9			0.353538			0.176769	+	0.984252i	$0.443435\pi$
$108$			1.26515e8i			0.00861042i
$109$	1.39855e10	−	1.39855e10i	0.908961	−	0.908961i	−0.0872273	−	0.996188i	$-0.527801\pi$
$109$	1.39855e10	−	1.39855e10i	0.908961	−	0.908961i	0.996188	+	0.0872273i	$0.0278006\pi$
$110$	−9.95477e9	+	9.95477e9i	−0.618113	+	0.618113i
$111$	2.95855e9	+	2.95855e9i	0.175576	+	0.175576i
$112$	1.86969e10	+	1.86969e10i	1.06091	+	1.06091i
$113$	−6.11828e9			−0.332076			−0.166038	−	0.986119i	$-0.553097\pi$
$113$	−6.11828e9			−0.332076			−0.166038	+	0.986119i	$0.553097\pi$
$114$		−	1.00139e10i		−	0.520089i
$115$	9.84045e9	+	9.84045e9i	0.489245	+	0.489245i
$116$		−	2.11645e8i		−	0.0100767i
$117$	4.88329e9	+	1.86084e10i	0.222733	+	0.848751i
$118$	1.72756e10			0.755131
$119$	−1.87284e10	+	1.87284e10i	−0.784814	+	0.784814i
$120$	5.48398e9			0.220389
$121$			2.27516e10i			0.877172i
$122$	1.72891e10	−	1.72891e10i	0.639695	−	0.639695i
$123$	−6.62404e9	+	6.62404e9i	−0.235287	+	0.235287i
$124$	2.75770e8	+	2.75770e8i	0.00940672	+	0.00940672i
$125$	−2.18610e10	−	2.18610e10i	−0.716342	−	0.716342i
$126$	4.15465e10			1.30822
$127$		−	6.86562e9i		−	0.207808i	−0.994587	−	0.103904i	$-0.966867\pi$
$127$		−	6.86562e9i		−	0.207808i	0.994587	−	0.103904i	$-0.0331334\pi$
$128$	−2.47625e10	−	2.47625e10i	−0.720685	−	0.720685i
$129$		−	5.50389e9i		−	0.154071i
$130$	−2.29132e10	+	6.01297e9i	−0.617119	+	0.161947i
$131$	3.45446e9			0.0895413			0.0447706	−	0.998997i	$-0.485744\pi$
$131$	3.45446e9			0.0895413			0.0447706	+	0.998997i	$0.485744\pi$
$132$	−1.78055e8	+	1.78055e8i	−0.00444308	+	0.00444308i
$133$	−9.09988e10			−2.18664
$134$		−	2.89563e10i		−	0.670223i
$135$	1.32076e10	−	1.32076e10i	0.294546	−	0.294546i
$136$	2.44876e10	−	2.44876e10i	0.526322	−	0.526322i
$137$	−1.68243e10	−	1.68243e10i	−0.348605	−	0.348605i	0.510985	−	0.859590i	$-0.329281\pi$
$137$	−1.68243e10	−	1.68243e10i	−0.348605	−	0.348605i	−0.859590	+	0.510985i	$0.829281\pi$
$138$	1.36092e10	+	1.36092e10i	0.271917	+	0.271917i
$139$	3.70961e10			0.714914			0.357457	−	0.933930i	$-0.383644\pi$
$139$	3.70961e10			0.714914			0.357457	+	0.933930i	$0.383644\pi$
$140$			6.61634e8i			0.0123021i
$141$	2.13455e10	+	2.13455e10i	0.383011	+	0.383011i
$142$		−	7.21783e10i		−	1.25016i
$143$	−4.13297e10	+	7.07393e10i	−0.691166	+	1.18299i
$144$	−5.50344e10			−0.888836
$145$	−2.20946e10	+	2.20946e10i	−0.344704	+	0.344704i
$146$	−9.55763e10			−1.44074
$147$			2.86854e10i			0.417902i
$148$	4.66709e8	−	4.66709e8i	0.00657260	−	0.00657260i
$149$	4.95312e10	−	4.95312e10i	0.674446	−	0.674446i	−0.284292	−	0.958738i	$-0.591758\pi$
$149$	4.95312e10	−	4.95312e10i	0.674446	−	0.674446i	0.958738	+	0.284292i	$0.0917585\pi$
$150$	−1.13163e10	−	1.13163e10i	−0.149021	−	0.149021i
$151$	1.05811e11	+	1.05811e11i	1.34786	+	1.34786i	0.887983	+	0.459877i	$0.152107\pi$
$151$	1.05811e11	+	1.05811e11i	1.34786	+	1.34786i	0.459877	+	0.887983i	$0.347893\pi$
$152$	1.18982e11			1.46643
$153$		−	5.51273e10i		−	0.657521i
$154$	1.25107e11	+	1.25107e11i	1.44437	+	1.44437i
$155$		−	5.75779e10i		−	0.643572i
$156$	−4.09834e8	+	1.07550e8i	−0.00443593	+	0.00116410i
$157$	−9.59586e10			−1.00597			−0.502985	−	0.864295i	$-0.667765\pi$
$157$	−9.59586e10			−1.00597			−0.502985	+	0.864295i	$0.667765\pi$
$158$	−8.12713e10	+	8.12713e10i	−0.825376	+	0.825376i
$159$	−1.80797e10			−0.177912
$160$		−	1.74167e9i		−	0.0166099i
$161$	1.23670e11	−	1.23670e11i	1.14324	−	1.14324i
$162$	−5.14175e10	+	5.14175e10i	−0.460825	+	0.460825i
$163$	6.85990e10	+	6.85990e10i	0.596184	+	0.596184i	0.939295	−	0.343111i	$-0.111481\pi$
$163$	6.85990e10	+	6.85990e10i	0.596184	+	0.596184i	−0.343111	+	0.939295i	$0.611481\pi$
$164$	1.04494e9	+	1.04494e9i	0.00880786	+	0.00880786i
$165$	3.71760e10			0.303979
$166$		−	1.41760e11i		−	1.12464i
$167$	−2.05734e10	−	2.05734e10i	−0.158388	−	0.158388i	0.623464	−	0.781852i	$-0.285725\pi$
$167$	−2.05734e10	−	2.05734e10i	−0.158388	−	0.158388i	−0.781852	+	0.623464i	$0.785725\pi$
$168$		−	6.89201e10i		−	0.514991i
$169$	−1.20094e11	+	6.76930e10i	−0.871141	+	0.491032i
$170$	6.78802e10			0.478078
$171$	1.33928e11	−	1.33928e11i	0.915990	−	0.915990i
$172$	−8.68234e8			−0.00576759
$173$			1.53965e11i			0.993556i	0.867878	+	0.496778i	$0.165484\pi$
$173$			1.53965e11i			0.993556i	−0.867878	+	0.496778i	$0.834516\pi$
$174$	−3.05564e10	+	3.05564e10i	−0.191583	+	0.191583i
$175$	−1.02834e11	+	1.02834e11i	−0.626536	+	0.626536i
$176$	−1.65722e11	−	1.65722e11i	−0.981334	−	0.981334i
$177$	−3.22578e10	−	3.22578e10i	−0.185681	−	0.185681i
$178$	−2.34104e9			−0.0131012
$179$			2.37704e10i			0.129351i	0.997906	+	0.0646757i	$0.0206013\pi$
$179$			2.37704e10i			0.129351i	−0.997906	+	0.0646757i	$0.979399\pi$
$180$	−9.73763e8	−	9.73763e8i	−0.00515336	−	0.00515336i
$181$		−	1.14912e11i		−	0.591526i	−0.955261	−	0.295763i	$-0.904426\pi$
$181$		−	1.14912e11i		−	0.591526i	0.955261	−	0.295763i	$-0.0955738\pi$
$182$	7.55682e10	+	2.87962e11i	0.378427	+	1.44204i
$183$	−6.45659e10			−0.314592
$184$	−1.61700e11	+	1.61700e11i	−0.766691	+	0.766691i
$185$	−9.74440e10			−0.449673
$186$		−	7.96291e10i		−	0.357690i
$187$	1.66002e11	−	1.66002e11i	0.725947	−	0.725947i
$188$	3.36723e9	−	3.36723e9i	0.0143378	−	0.0143378i
$189$	−1.65986e11	−	1.65986e11i	−0.688277	−	0.688277i
$190$	1.64910e11	+	1.64910e11i	0.666008	+	0.666008i
$191$	3.09078e11			1.21591			0.607956	−	0.793971i	$-0.291990\pi$
$191$	3.09078e11			1.21591			0.607956	+	0.793971i	$0.291990\pi$
$192$			9.00980e10i			0.345310i
$193$	−3.02659e11	−	3.02659e11i	−1.13023	−	1.13023i	−0.990138	−	0.140094i	$-0.955260\pi$
$193$	−3.02659e11	−	3.02659e11i	−1.13023	−	1.13023i	−0.140094	−	0.990138i	$-0.544740\pi$
$194$		−	2.33295e11i		−	0.848979i
$195$	5.40123e10	+	3.15569e10i	0.191566	+	0.111923i
$196$	4.52509e9			0.0156440
$197$	−2.43484e11	+	2.43484e11i	−0.820616	+	0.820616i	−0.986196	−	0.165581i	$-0.947050\pi$
$197$	−2.43484e11	+	2.43484e11i	−0.820616	+	0.820616i	0.165581	+	0.986196i	$0.447050\pi$
$198$	−3.68253e11			−1.21010
$199$		−	3.45102e11i		−	1.10581i	−0.833243	−	0.552907i	$-0.813518\pi$
$199$		−	3.45102e11i		−	1.10581i	0.833243	−	0.552907i	$-0.186482\pi$
$200$	1.34456e11	−	1.34456e11i	0.420176	−	0.420176i
$201$	−5.40686e10	+	5.40686e10i	−0.164803	+	0.164803i
$202$	1.84671e11	+	1.84671e11i	0.549088	+	0.549088i
$203$	2.77675e11	+	2.77675e11i	0.805482	+	0.805482i
$204$	1.21413e9			0.00343649
$205$		−	2.18172e11i		−	0.602601i
$206$	2.77270e11	+	2.77270e11i	0.747423	+	0.747423i
$207$			3.64024e11i			0.957809i
$208$	−1.00101e11	−	3.81448e11i	−0.257112	−	0.979757i
$209$	8.06580e11			2.02263
$210$	9.55241e10	−	9.55241e10i	0.233893	−	0.233893i
$211$	−4.77173e10			−0.114094			−0.0570471	−	0.998371i	$-0.518169\pi$
$211$	−4.77173e10			−0.114094			−0.0570471	+	0.998371i	$0.518169\pi$
$212$			2.85205e9i			0.00666005i
$213$	−1.34775e11	+	1.34775e11i	−0.307404	+	0.307404i
$214$	−1.12932e11	+	1.12932e11i	−0.251621	+	0.251621i
$215$	9.06392e10	+	9.06392e10i	0.197298	+	0.197298i
$216$	2.17029e11	+	2.17029e11i	0.461581	+	0.461581i
$217$	−7.23612e11			−1.50386
$218$			6.37044e11i			1.29386i
$219$	1.78464e11	+	1.78464e11i	0.354267	+	0.354267i
$220$		−	5.86448e9i		−	0.0113793i
$221$	3.82092e11	−	1.00270e11i	0.724780	−	0.190200i
$222$	−1.34763e11			−0.249923
$223$	2.01194e11	−	2.01194e11i	0.364830	−	0.364830i	−0.500758	−	0.865588i	$-0.666945\pi$
$223$	2.01194e11	−	2.01194e11i	0.364830	−	0.364830i	0.865588	+	0.500758i	$0.166945\pi$
$224$	−2.18885e10			−0.0388129
$225$		−	3.02693e11i		−	0.524916i
$226$	1.39345e11	−	1.39345e11i	0.236346	−	0.236346i
$227$	−2.19125e11	+	2.19125e11i	−0.363549	+	0.363549i	−0.865118	−	0.501569i	$-0.832756\pi$
$227$	−2.19125e11	+	2.19125e11i	−0.363549	+	0.363549i	0.501569	+	0.865118i	$0.332756\pi$
$228$	2.94965e9	+	2.94965e9i	0.00478736	+	0.00478736i
$229$	2.74341e11	+	2.74341e11i	0.435625	+	0.435625i	0.890537	−	0.454911i	$-0.150329\pi$
$229$	2.74341e11	+	2.74341e11i	0.435625	+	0.435625i	−0.454911	+	0.890537i	$0.650329\pi$
$230$	−4.48236e11			−0.696414
$231$		−	4.67210e11i		−	0.710318i
$232$	−3.63062e11	−	3.63062e11i	−0.540183	−	0.540183i
$233$		−	5.67118e11i		−	0.825836i	−0.910768	−	0.412918i	$-0.864510\pi$
$233$		−	5.67118e11i		−	0.825836i	0.910768	−	0.412918i	$-0.135490\pi$
$234$	−5.35028e11	−	3.12592e11i	−0.762601	−	0.445552i
$235$	−7.03043e11			−0.980941
$236$	−5.08863e9	+	5.08863e9i	−0.00695089	+	0.00695089i
$237$	3.03507e11			0.405908
$238$		−	8.53086e11i		−	1.11714i
$239$	−7.76835e11	+	7.76835e11i	−0.996183	+	0.996183i	−0.999993	−	0.00380977i	$-0.998787\pi$
$239$	−7.76835e11	+	7.76835e11i	−0.996183	+	0.996183i	0.00380977	+	0.999993i	$0.498787\pi$
$240$	−1.26535e11	+	1.26535e11i	−0.158912	+	0.158912i
$241$	−4.62402e11	−	4.62402e11i	−0.568767	−	0.568767i	0.363016	−	0.931783i	$-0.381747\pi$
$241$	−4.62402e11	−	4.62402e11i	−0.568767	−	0.568767i	−0.931783	+	0.363016i	$0.881747\pi$
$242$	−5.18172e11	−	5.18172e11i	−0.624305	−	0.624305i
$243$	7.48814e11			0.883777
$244$			1.01852e10i			0.0117766i
$245$	−4.72396e11	−	4.72396e11i	−0.535151	−	0.535151i
$246$		−	3.01727e11i		−	0.334919i
$247$	1.17186e12	+	6.84666e11i	1.27465	+	0.744722i
$248$	9.46129e11			1.00854
$249$	−2.64700e11	+	2.64700e11i	−0.276540	+	0.276540i
$250$	9.95778e11			1.01968
$251$			3.90895e11i			0.392366i	0.980567	+	0.196183i	$0.0628547\pi$
$251$			3.90895e11i			0.392366i	−0.980567	+	0.196183i	$0.937145\pi$
$252$	−1.22378e10	+	1.22378e10i	−0.0120420	+	0.0120420i
$253$	−1.09617e12	+	1.09617e12i	−1.05748	+	1.05748i
$254$	1.56366e11	+	1.56366e11i	0.147902	+	0.147902i
$255$	−1.26749e11	−	1.26749e11i	−0.117556	−	0.117556i
$256$	4.32122e10			0.0393013
$257$			5.43161e11i			0.484466i	0.970218	+	0.242233i	$0.0778798\pi$
$257$			5.43161e11i			0.484466i	−0.970218	+	0.242233i	$0.922120\pi$
$258$	1.25352e11	+	1.25352e11i	0.109656	+	0.109656i
$259$			1.22463e12i			1.05077i
$260$	4.97807e9	−	8.52038e9i	0.00418981	−	0.00717121i
$261$	−8.17338e11			−0.674837
$262$	−7.86759e10	+	7.86759e10i	−0.0637287	+	0.0637287i
$263$	1.79873e12			1.42951			0.714753	−	0.699377i	$-0.246539\pi$
$263$	1.79873e12			1.42951			0.714753	+	0.699377i	$0.246539\pi$
$264$			6.10882e11i			0.476363i
$265$	2.97739e11	−	2.97739e11i	0.227828	−	0.227828i
$266$	2.07251e12	−	2.07251e12i	1.55629	−	1.55629i
$267$	4.37131e9	+	4.37131e9i	0.00322148	+	0.00322148i
$268$	8.52926e9	+	8.52926e9i	0.00616932	+	0.00616932i
$269$	−1.51262e12			−1.07391			−0.536956	−	0.843610i	$-0.680426\pi$
$269$	−1.51262e12			−1.07391			−0.536956	+	0.843610i	$0.680426\pi$
$270$			6.01609e11i			0.419271i
$271$	−2.80512e11	−	2.80512e11i	−0.191914	−	0.191914i	0.604609	−	0.796522i	$-0.293329\pi$
$271$	−2.80512e11	−	2.80512e11i	−0.191914	−	0.191914i	−0.796522	+	0.604609i	$0.793329\pi$
$272$			1.13004e12i			0.759010i
$273$	3.96592e11	−	6.78801e11i	0.261536	−	0.447640i
$274$	7.66352e11			0.496221
$275$	9.11482e11	−	9.11482e11i	0.579542	−	0.579542i
$276$	−8.01732e9			−0.00500592
$277$			1.96089e12i			1.20241i	0.799094	+	0.601206i	$0.205313\pi$
$277$			1.96089e12i			1.20241i	−0.799094	+	0.601206i	$0.794687\pi$
$278$	−8.44870e11	+	8.44870e11i	−0.508822	+	0.508822i
$279$	1.06498e12	−	1.06498e12i	0.629970	−	0.629970i
$280$	1.13499e12	+	1.13499e12i	0.659480	+	0.659480i
$281$	−2.13017e12	−	2.13017e12i	−1.21586	−	1.21586i	−0.969069	−	0.246788i	$-0.920625\pi$
$281$	−2.13017e12	−	2.13017e12i	−1.21586	−	1.21586i	−0.246788	−	0.969069i	$-0.579375\pi$
$282$	−9.72295e11			−0.545196
$283$			1.73966e11i			0.0958368i	0.998851	+	0.0479184i	$0.0152587\pi$
$283$			1.73966e11i			0.0958368i	−0.998851	+	0.0479184i	$0.984741\pi$
$284$	2.12606e10	+	2.12606e10i	0.0115076	+	0.0115076i
$285$		−	6.15856e11i		−	0.327533i
$286$	−6.69809e11	−	2.55239e12i	−0.350042	−	1.33388i
$287$	−2.74188e12			−1.40812
$288$	3.22145e10	−	3.22145e10i	0.0162588	−	0.0162588i
$289$	8.84050e11			0.438518
$290$		−	1.00642e12i		−	0.490668i
$291$	−4.35619e11	+	4.35619e11i	−0.208758	+	0.208758i
$292$	2.81526e10	−	2.81526e10i	0.0132618	−	0.0132618i
$293$	1.25194e12	+	1.25194e12i	0.579755	+	0.579755i	0.934836	−	0.355081i	$-0.115547\pi$
$293$	1.25194e12	+	1.25194e12i	0.579755	+	0.579755i	−0.355081	+	0.934836i	$0.615547\pi$
$294$	−6.53315e11	−	6.53315e11i	−0.297431	−	0.297431i
$295$	1.06245e12			0.475554
$296$		−	1.60122e12i		−	0.704679i
$297$	1.47124e12	+	1.47124e12i	0.636651	+	0.636651i
$298$			2.25616e12i			0.960039i
$299$	−2.52308e12	+	6.62117e11i	−1.05578	+	0.277063i
$300$	6.66654e9			0.00274343
$301$	1.13911e12	−	1.13911e12i	0.461034	−	0.461034i
$302$	−4.81971e12			−1.91861
$303$		−	6.89653e11i		−	0.270033i
$304$	−2.74534e12	+	2.74534e12i	−1.05737	+	1.05737i
$305$	1.06328e12	−	1.06328e12i	0.402856	−	0.402856i
$306$	1.25553e12	+	1.25553e12i	0.467974	+	0.467974i
$307$	−2.59459e12	−	2.59459e12i	−0.951429	−	0.951429i	0.0474445	−	0.998874i	$-0.484892\pi$
$307$	−2.59459e12	−	2.59459e12i	−0.951429	−	0.951429i	−0.998874	+	0.0474445i	$0.984892\pi$
$308$	−7.37020e10			−0.0265904
$309$		−	1.03546e12i		−	0.367571i
$310$	1.31135e12	+	1.31135e12i	0.458046	+	0.458046i
$311$			3.08415e12i			1.06007i	0.847977	+	0.530034i	$0.177821\pi$
$311$			3.08415e12i			1.06007i	−0.847977	+	0.530034i	$0.822179\pi$
$312$	−5.18548e11	+	8.87538e11i	−0.175394	+	0.300202i
$313$	3.47778e12			1.15766			0.578829	−	0.815449i	$-0.303510\pi$
$313$	3.47778e12			1.15766			0.578829	+	0.815449i	$0.303510\pi$
$314$	2.18547e12	−	2.18547e12i	0.715974	−	0.715974i
$315$	2.55513e12			0.823872
$316$		−	4.78779e10i		−	0.0151950i
$317$	2.76452e12	−	2.76452e12i	0.863622	−	0.863622i	−0.128135	−	0.991757i	$-0.540899\pi$
$317$	2.76452e12	−	2.76452e12i	0.863622	−	0.863622i	0.991757	+	0.128135i	$0.0408991\pi$
$318$	4.11767e11	−	4.11767e11i	0.126624	−	0.126624i
$319$	−2.46121e12	−	2.46121e12i	−0.745065	−	0.745065i
$320$	−1.48375e12	−	1.48375e12i	−0.442192	−	0.442192i
$321$	4.21743e11			0.123744
$322$			5.63322e12i			1.62734i
$323$	−2.74998e12	−	2.74998e12i	−0.782198	−	0.782198i
$324$		−	3.02907e10i		−	0.00848368i
$325$	2.09799e12	−	5.50562e11i	0.578610	−	0.151841i
$326$	−3.12471e12			−0.848637
$327$	1.18952e12	−	1.18952e12i	0.318150	−	0.318150i
$328$	3.58504e12			0.944331
$329$			8.83551e12i			2.29220i
$330$	−8.46690e11	+	8.46690e11i	−0.216349	+	0.216349i
$331$	2.96259e12	−	2.96259e12i	0.745644	−	0.745644i	−0.228014	−	0.973658i	$-0.573223\pi$
$331$	2.96259e12	−	2.96259e12i	0.745644	−	0.745644i	0.973658	+	0.228014i	$0.0732232\pi$
$332$	4.17562e10	+	4.17562e10i	0.0103522	+	0.0103522i
$333$	−1.80236e12	−	1.80236e12i	−0.440169	−	0.440169i
$334$	9.37124e11			0.225458
$335$		−	1.78082e12i		−	0.422082i
$336$	1.59024e12	+	1.59024e12i	0.371335	+	0.371335i
$337$			4.79696e12i			1.10361i	0.833973	+	0.551806i	$0.186061\pi$
$337$			4.79696e12i			1.10361i	−0.833973	+	0.551806i	$0.813939\pi$
$338$	1.19345e12	−	4.27689e12i	0.270533	−	0.969492i
$339$	−5.20383e11			−0.116232
$340$	−1.99945e10	+	1.99945e10i	−0.00440065	+	0.00440065i
$341$	6.41383e12			1.39106
$342$			6.10047e12i			1.30386i
$343$	−9.64417e11	+	9.64417e11i	−0.203139	+	0.203139i
$344$	−1.48940e12	+	1.48940e12i	−0.309185	+	0.309185i
$345$	8.36967e11	+	8.36967e11i	0.171243	+	0.171243i
$346$	−3.50659e12	−	3.50659e12i	−0.707138	−	0.707138i
$347$	−2.14334e12			−0.426034			−0.213017	−	0.977048i	$-0.568329\pi$
$347$	−2.14334e12			−0.426034			−0.213017	+	0.977048i	$0.568329\pi$
$348$		−	1.80012e10i		−	0.00352699i
$349$	−2.03902e12	−	2.03902e12i	−0.393817	−	0.393817i	0.482228	−	0.876046i	$-0.339828\pi$
$349$	−2.03902e12	−	2.03902e12i	−0.393817	−	0.393817i	−0.876046	+	0.482228i	$0.839828\pi$
$350$		−	4.68412e12i		−	0.891842i
$351$	8.88673e11	+	3.38640e12i	0.166804	+	0.635628i
$352$	1.94011e11			0.0359016
$353$	−4.43529e12	+	4.43529e12i	−0.809186	+	0.809186i	−0.984511	−	0.175325i	$-0.943902\pi$
$353$	−4.43529e12	+	4.43529e12i	−0.809186	+	0.809186i	0.175325	+	0.984511i	$0.443902\pi$
$354$	1.46935e12			0.264308
$355$		−	4.43899e12i		−	0.787304i
$356$	6.89569e8	−	6.89569e8i	0.000120595	−	0.000120595i
$357$	−1.59292e12	+	1.59292e12i	−0.274697	+	0.274697i
$358$	−5.41375e11	−	5.41375e11i	−0.0920625	−	0.0920625i
$359$	3.03980e12	+	3.03980e12i	0.509769	+	0.509769i	0.914455	−	0.404687i	$-0.132619\pi$
$359$	3.03980e12	+	3.03980e12i	0.509769	+	0.509769i	−0.404687	+	0.914455i	$0.632619\pi$
$360$	−3.34085e12			−0.552516
$361$		−	7.23070e12i		−	1.17935i
$362$	2.61715e12	+	2.61715e12i	0.421003	+	0.421003i
$363$			1.93511e12i			0.307024i
$364$	−1.07080e11	−	6.25620e10i	−0.0167572	−	0.00979047i
$365$	−5.87797e12			−0.907326
$366$	1.47050e12	−	1.47050e12i	0.223903	−	0.223903i
$367$	−8.81460e12			−1.32395			−0.661976	−	0.749525i	$-0.730282\pi$
$367$	−8.81460e12			−1.32395			−0.661976	+	0.749525i	$0.730282\pi$
$368$		−	7.46201e12i		−	1.10565i
$369$	4.03538e12	−	4.03538e12i	0.589865	−	0.589865i
$370$	2.21931e12	−	2.21931e12i	0.320043	−	0.320043i
$371$	−3.74185e12	−	3.74185e12i	−0.532373	−	0.532373i
$372$	2.34552e10	+	2.34552e10i	0.00329250	+	0.00329250i
$373$	−4.51298e12			−0.625056			−0.312528	−	0.949909i	$-0.601176\pi$
$373$	−4.51298e12			−0.625056			−0.312528	+	0.949909i	$0.601176\pi$
$374$			7.56144e12i			1.03335i
$375$	−1.85936e12	−	1.85936e12i	−0.250731	−	0.250731i
$376$		−	1.15525e13i		−	1.53723i
$377$	−1.48664e12	−	5.66503e12i	−0.195209	−	0.743868i
$378$	7.56073e12			0.979726
$379$	1.13902e11	−	1.13902e11i	0.0145658	−	0.0145658i	−0.699786	−	0.714352i	$-0.746721\pi$
$379$	1.13902e11	−	1.13902e11i	0.0145658	−	0.0145658i	0.714352	+	0.699786i	$0.246721\pi$
$380$	−9.71507e10			−0.0122611
$381$		−	5.83947e11i		−	0.0727358i
$382$	−7.03932e12	+	7.03932e12i	−0.865394	+	0.865394i
$383$	−8.36863e12	+	8.36863e12i	−1.01545	+	1.01545i	−0.0155760	+	0.999879i	$0.504958\pi$
$383$	−8.36863e12	+	8.36863e12i	−1.01545	+	1.01545i	−0.999879	+	0.0155760i	$0.995042\pi$
$384$	−2.10615e12	−	2.10615e12i	−0.252251	−	0.252251i
$385$	7.69411e12	+	7.69411e12i	0.909609	+	0.909609i
$386$	1.37862e13			1.60883
$387$			3.35298e12i			0.386257i
$388$	6.87185e10	+	6.87185e10i	0.00781475	+	0.00781475i
$389$			1.05416e13i			1.18347i	0.806132	+	0.591735i	$0.201557\pi$
$389$			1.05416e13i			1.18347i	−0.806132	+	0.591735i	$0.798443\pi$
$390$	−1.94885e12	+	5.11426e11i	−0.216001	+	0.0566839i
$391$	7.47461e12			0.817909
$392$	7.76249e12	−	7.76249e12i	0.838631	−	0.838631i
$393$	2.93814e11			0.0313408
$394$		−	1.10908e13i		−	1.16810i
$395$	−4.99821e12	+	4.99821e12i	−0.519792	+	0.519792i
$396$	1.08471e11	−	1.08471e11i	0.0111388	−	0.0111388i
$397$	1.18311e13	+	1.18311e13i	1.19970	+	1.19970i	0.974257	+	0.225442i	$0.0723825\pi$
$397$	1.18311e13	+	1.18311e13i	1.19970	+	1.19970i	0.225442	+	0.974257i	$0.427617\pi$
$398$	7.85976e12	+	7.85976e12i	0.787035	+	0.787035i
$399$	−7.73979e12			−0.765358
$400$			6.20479e12i			0.605937i
$401$	7.15140e12	+	7.15140e12i	0.689714	+	0.689714i	0.962169	−	0.272454i	$-0.0878354\pi$
$401$	7.15140e12	+	7.15140e12i	0.689714	+	0.689714i	−0.272454	+	0.962169i	$0.587835\pi$
$402$		−	2.46284e12i		−	0.234588i
$403$	9.31852e12	+	5.44438e12i	0.876641	+	0.512181i
$404$	−1.08792e11			−0.0101086
$405$	−3.16219e12	+	3.16219e12i	−0.290211	+	0.290211i
$406$	−1.26482e13			−1.14656
$407$		−	1.08547e13i		−	0.971952i
$408$	2.08276e12	−	2.08276e12i	0.184221	−	0.184221i
$409$	−5.81271e11	+	5.81271e11i	−0.0507881	+	0.0507881i	−0.732045	−	0.681257i	$-0.761434\pi$
$409$	−5.81271e11	+	5.81271e11i	−0.0507881	+	0.0507881i	0.681257	+	0.732045i	$0.261434\pi$
$410$	4.96890e12	+	4.96890e12i	0.428885	+	0.428885i
$411$	−1.43097e12	−	1.43097e12i	−0.122017	−	0.122017i
$412$	−1.63343e11			−0.0137599
$413$		−	1.33524e13i		−	1.11124i
$414$	−8.29072e12	−	8.29072e12i	−0.681696	−	0.681696i
$415$		−	8.71828e12i		−	0.708256i
$416$	2.81875e11	+	1.64687e11i	0.0226251	+	0.0132188i
$417$	3.15516e12			0.250231
$418$	−1.83700e13	+	1.83700e13i	−1.43955	+	1.43955i
$419$	1.49944e13			1.16107			0.580536	−	0.814234i	$-0.302843\pi$
$419$	1.49944e13			1.16107			0.580536	+	0.814234i	$0.302843\pi$
$420$			5.62744e10i			0.00430591i
$421$	9.96229e12	−	9.96229e12i	0.753266	−	0.753266i	−0.221821	−	0.975087i	$-0.571200\pi$
$421$	9.96229e12	−	9.96229e12i	0.753266	−	0.753266i	0.975087	+	0.221821i	$0.0712001\pi$
$422$	1.08677e12	−	1.08677e12i	0.0812036	−	0.0812036i
$423$	−1.30037e13	−	1.30037e13i	−0.960209	−	0.960209i
$424$	4.89250e12	+	4.89250e12i	0.357027	+	0.357027i
$425$	−6.21527e12			−0.448245
$426$		−	6.13903e12i		−	0.437574i
$427$	−1.33628e13	−	1.33628e13i	−0.941369	−	0.941369i
$428$		−	6.65295e10i		−	0.00463229i
$429$	−3.51524e12	+	6.01664e12i	−0.241919	+	0.414064i
$430$	−4.12865e12			−0.280844
$431$	−8.54567e12	+	8.54567e12i	−0.574592	+	0.574592i	−0.933408	−	0.358816i	$-0.883181\pi$
$431$	−8.54567e12	+	8.54567e12i	−0.574592	+	0.574592i	0.358816	+	0.933408i	$0.383181\pi$
$432$	−1.00153e13			−0.665647
$433$		−	3.03594e12i		−	0.199459i	−0.995015	−	0.0997294i	$-0.968202\pi$
$433$		−	3.03594e12i		−	0.199459i	0.995015	−	0.0997294i	$-0.0317977\pi$
$434$	1.64804e13	−	1.64804e13i	1.07033	−	1.07033i
$435$	−1.87923e12	+	1.87923e12i	−0.120652	+	0.120652i
$436$	−1.87645e11	−	1.87645e11i	−0.0119098	−	0.0119098i
$437$	1.81590e13	+	1.81590e13i	1.13943	+	1.13943i
$438$	−8.12912e12			−0.504281
$439$			7.50557e12i			0.460321i	0.973153	+	0.230161i	$0.0739251\pi$
$439$			7.50557e12i			0.460321i	−0.973153	+	0.230161i	$0.926075\pi$
$440$	−1.00601e13	−	1.00601e13i	−0.610014	−	0.610014i
$441$		−	1.74752e13i		−	1.04768i
$442$	−6.41854e12	+	1.09859e13i	−0.380474	+	0.651213i
$443$	−3.30503e12			−0.193712			−0.0968561	−	0.995298i	$-0.530879\pi$
$443$	−3.30503e12			−0.193712			−0.0968561	+	0.995298i	$0.530879\pi$
$444$	3.96953e10	−	3.96953e10i	0.00230051	−	0.00230051i
$445$	−1.43975e11			−0.00825063
$446$			9.16445e12i			0.519317i
$447$	4.21281e12	−	4.21281e12i	0.236066	−	0.236066i
$448$	−1.86471e13	+	1.86471e13i	−1.03329	+	1.03329i
$449$	−1.67202e13	−	1.67202e13i	−0.916239	−	0.916239i	0.0805141	−	0.996753i	$-0.474344\pi$
$449$	−1.67202e13	−	1.67202e13i	−0.916239	−	0.916239i	−0.996753	+	0.0805141i	$0.974344\pi$
$450$	6.89388e12	+	6.89388e12i	0.373595	+	0.373595i
$451$	2.43030e13			1.30250
$452$			8.20898e10i			0.00435108i
$453$	8.99959e12	+	8.99959e12i	0.471771	+	0.471771i
$454$		−	9.98123e12i		−	0.517493i
$455$	4.64747e12	+	1.77098e13i	0.238319	+	0.908147i
$456$	1.01198e13			0.513274
$457$	−1.29793e12	+	1.29793e12i	−0.0651133	+	0.0651133i	−0.738914	−	0.673800i	$-0.764661\pi$
$457$	−1.29793e12	+	1.29793e12i	−0.0651133	+	0.0651133i	0.673800	+	0.738914i	$0.264661\pi$
$458$	−1.24963e13			−0.620090
$459$		−	1.00322e13i		−	0.492416i
$460$	1.32031e11	−	1.32031e11i	0.00641041	−	0.00641041i
$461$	−9.46842e11	+	9.46842e11i	−0.0454750	+	0.0454750i	−0.729479	−	0.684004i	$-0.760237\pi$
$461$	−9.46842e11	+	9.46842e11i	−0.0454750	+	0.0454750i	0.684004	+	0.729479i	$0.260237\pi$
$462$	1.06408e13	+	1.06408e13i	0.505550	+	0.505550i
$463$	−3.48553e12	−	3.48553e12i	−0.163819	−	0.163819i	0.620437	−	0.784256i	$-0.286955\pi$
$463$	−3.48553e12	−	3.48553e12i	−0.163819	−	0.163819i	−0.784256	+	0.620437i	$0.786955\pi$
$464$	1.67543e13			0.779000
$465$		−	4.89721e12i		−	0.225260i
$466$	1.29162e13	+	1.29162e13i	0.587767	+	0.587767i
$467$		−	7.88956e12i		−	0.355196i	−0.984103	−	0.177598i	$-0.943167\pi$
$467$		−	7.88956e12i		−	0.355196i	0.984103	−	0.177598i	$-0.0568327\pi$
$468$	2.49672e11	−	6.55198e10i	0.0111209	−	0.00291839i
$469$	−2.23805e13			−0.986294
$470$	1.60119e13	−	1.60119e13i	0.698159	−	0.698159i
$471$	−8.16163e12			−0.352105
$472$			1.74584e13i			0.745237i
$473$	−1.00966e13	+	1.00966e13i	−0.426453	+	0.426453i
$474$	−6.91243e12	+	6.91243e12i	−0.288894	+	0.288894i
$475$	−1.50996e13	−	1.50996e13i	−0.624448	−	0.624448i
$476$	2.51282e11	+	2.51282e11i	0.0102832	+	0.0102832i
$477$	1.10142e13			0.446025
$478$		−	3.53851e13i		−	1.41802i
$479$	3.13440e13	+	3.13440e13i	1.24302	+	1.24302i	0.958744	+	0.284271i	$0.0917517\pi$
$479$	3.13440e13	+	3.13440e13i	1.24302	+	1.24302i	0.284271	+	0.958744i	$0.408248\pi$
$480$		−	1.48136e11i		−	0.00581371i
$481$	9.21400e12	−	1.57705e13i	0.357868	−	0.612521i
$482$	2.10626e13			0.809610
$483$	1.05186e13	−	1.05186e13i	0.400150	−	0.400150i
$484$	3.05261e11			0.0114933
$485$		−	1.43477e13i		−	0.534656i
$486$	−1.70544e13	+	1.70544e13i	−0.629005	+	0.629005i
$487$	2.47115e13	−	2.47115e13i	0.902098	−	0.902098i	−0.0935194	−	0.995617i	$-0.529812\pi$
$487$	2.47115e13	−	2.47115e13i	0.902098	−	0.902098i	0.995617	+	0.0935194i	$0.0298117\pi$
$488$	1.74721e13	+	1.74721e13i	0.631313	+	0.631313i
$489$	5.83460e12	+	5.83460e12i	0.208673	+	0.208673i
$490$	2.15178e13			0.761759
$491$			2.16808e13i			0.759744i	0.925039	+	0.379872i	$0.124032\pi$
$491$			2.16808e13i			0.759744i	−0.925039	+	0.379872i	$0.875968\pi$
$492$	8.88757e10	+	8.88757e10i	0.00308288	+	0.00308288i
$493$			1.67826e13i			0.576269i
$494$	−4.22828e13	+	1.10960e13i	−1.43724	+	0.377166i
$495$	−2.26477e13			−0.762076
$496$	−2.18306e13	+	2.18306e13i	−0.727207	+	0.727207i
$497$	−5.57871e13			−1.83972
$498$		−	1.20572e13i		−	0.393640i
$499$	3.31595e13	−	3.31595e13i	1.07178	−	1.07178i	0.0745615	−	0.997216i	$-0.476244\pi$
$499$	3.31595e13	−	3.31595e13i	1.07178	−	1.07178i	0.997216	−	0.0745615i	$-0.0237557\pi$
$500$	−2.93312e11	+	2.93312e11i	−0.00938600	+	0.00938600i
$501$	−1.74984e12	−	1.74984e12i	−0.0554383	−	0.0554383i
$502$	−8.90270e12	−	8.90270e12i	−0.279256	−	0.279256i
$503$	−1.55928e12			−0.0484265			−0.0242133	−	0.999707i	$-0.507708\pi$
$503$	−1.55928e12			−0.0484265			−0.0242133	+	0.999707i	$0.507708\pi$
$504$			4.19862e13i			1.29108i
$505$	1.13573e13	+	1.13573e13i	0.345795	+	0.345795i
$506$		−	4.99308e13i		−	1.50527i
$507$	−1.02145e13	+	5.75754e12i	−0.304913	+	0.171869i
$508$	−9.21170e10			−0.00272283
$509$	−2.09520e13	+	2.09520e13i	−0.613250	+	0.613250i	−0.943791	−	0.330542i	$-0.892769\pi$
$509$	−2.09520e13	+	2.09520e13i	−0.613250	+	0.613250i	0.330542	+	0.943791i	$0.392769\pi$
$510$	5.77346e12			0.167335
$511$			7.38716e13i			2.12018i
$512$	2.43727e13	−	2.43727e13i	0.692713	−	0.692713i
$513$	2.43725e13	−	2.43725e13i	0.685983	−	0.685983i
$514$	−1.23706e13	−	1.23706e13i	−0.344806	−	0.344806i
$515$	1.70522e13	+	1.70522e13i	0.470699	+	0.470699i
$516$	−7.38465e10			−0.00201874
$517$		−	7.83147e13i		−	2.12027i
$518$	−2.78912e13	−	2.78912e13i	−0.747856	−	0.747856i
$519$			1.30953e13i			0.347760i
$520$	−6.07661e12	−	2.31557e13i	−0.159825	−	0.609033i
$521$	−1.41696e13			−0.369122			−0.184561	−	0.982821i	$-0.559086\pi$
$521$	−1.41696e13			−0.369122			−0.184561	+	0.982821i	$0.559086\pi$
$522$	1.86150e13	−	1.86150e13i	0.480298	−	0.480298i
$523$	−5.80721e13			−1.48409			−0.742044	−	0.670352i	$-0.766143\pi$
$523$	−5.80721e13			−1.48409			−0.742044	+	0.670352i	$0.766143\pi$
$524$		−	4.63489e10i		−	0.00117323i
$525$	−8.74641e12	+	8.74641e12i	−0.219297	+	0.219297i
$526$	−4.09663e13	+	4.09663e13i	−1.01741	+	1.01741i
$527$	−2.18675e13	−	2.18675e13i	−0.537955	−	0.537955i
$528$	−1.40953e13	−	1.40953e13i	−0.343482	−	0.343482i
$529$	−7.93088e12			−0.191444
$530$			1.35621e13i			0.324301i
$531$	1.96515e13	+	1.96515e13i	0.465503	+	0.465503i
$532$			1.22094e12i			0.0286508i
$533$	3.53094e13	+	2.06296e13i	0.820832	+	0.479574i
$534$	−1.99114e11			−0.00458560
$535$	−6.94535e12	+	6.94535e12i	−0.158462	+	0.158462i
$536$	2.92628e13			0.661441
$537$			2.02176e12i			0.0452749i
$538$	3.44502e13	−	3.44502e13i	0.764329	−	0.764329i
$539$	5.26221e13	−	5.26221e13i	1.15671	−	1.15671i
$540$	−1.77208e11	−	1.77208e11i	−0.00385934	−	0.00385934i
$541$	−4.32172e13	−	4.32172e13i	−0.932545	−	0.932545i	0.0653191	−	0.997864i	$-0.479193\pi$
$541$	−4.32172e13	−	4.32172e13i	−0.932545	−	0.932545i	−0.997864	+	0.0653191i	$0.979193\pi$
$542$	1.27774e13			0.273179
$543$		−	9.77372e12i		−	0.207043i
$544$	−6.61469e11	−	6.61469e11i	−0.0138840	−	0.0138840i
$545$			3.91784e13i			0.814825i
$546$	6.42736e12	+	2.44923e13i	0.132455	+	0.504738i
$547$	6.22495e13			1.27116			0.635578	−	0.772036i	$-0.280762\pi$
$547$	6.22495e13			1.27116			0.635578	+	0.772036i	$0.280762\pi$
$548$	−2.25734e11	+	2.25734e11i	−0.00456766	+	0.00456766i
$549$	3.93337e13			0.788684
$550$			4.15183e13i			0.824948i
$551$	−4.07722e13	+	4.07722e13i	−0.802798	+	0.802798i
$552$	−1.37532e13	+	1.37532e13i	−0.268354	+	0.268354i
$553$	6.28152e13	+	6.28152e13i	1.21462	+	1.21462i
$554$	−4.46595e13	−	4.46595e13i	−0.855786	−	0.855786i
$555$	−8.28798e12			−0.157392
$556$		−	4.97723e11i		−	0.00936729i
$557$	−6.62941e13	−	6.62941e13i	−1.23651	−	1.23651i	−0.961416	−	0.275098i	$-0.911290\pi$
$557$	−6.62941e13	−	6.62941e13i	−1.23651	−	1.23651i	−0.275098	−	0.961416i	$-0.588710\pi$
$558$			4.85102e13i			0.896730i
$559$	−2.32398e13	+	6.09867e12i	−0.425768	+	0.111732i
$560$	−5.23766e13			−0.951037
$561$	1.41191e13	−	1.41191e13i	0.254093	−	0.254093i
$562$	9.70300e13			1.73071
$563$			2.94230e12i			0.0520169i	0.999662	+	0.0260085i	$0.00827969\pi$
$563$			2.94230e12i			0.0520169i	−0.999662	+	0.0260085i	$0.991720\pi$
$564$	2.86395e11	−	2.86395e11i	0.00501846	−	0.00501846i
$565$	8.56976e12	−	8.56976e12i	0.148842	−	0.148842i
$566$	−3.96211e12	−	3.96211e12i	−0.0682094	−	0.0682094i
$567$	3.97409e13	+	3.97409e13i	0.678145	+	0.678145i
$568$	7.29422e13			1.23378
$569$			9.31203e13i			1.56129i	0.624976	+	0.780644i	$0.285109\pi$
$569$			9.31203e13i			1.56129i	−0.624976	+	0.780644i	$0.714891\pi$
$570$	1.40262e13	+	1.40262e13i	0.233113	+	0.233113i
$571$			8.43012e13i			1.38884i	0.719568	+	0.694422i	$0.244340\pi$
$571$			8.43012e13i			1.38884i	−0.719568	+	0.694422i	$0.755660\pi$
$572$	9.49119e11	+	5.54526e11i	0.0155003	+	0.00905612i
$573$	2.62883e13			0.425587
$574$	6.24468e13	−	6.24468e13i	1.00219	−	1.00219i
$575$	4.10415e13			0.652957
$576$		−	5.48878e13i		−	0.865693i
$577$	−4.62979e13	+	4.62979e13i	−0.723906	+	0.723906i	−0.969399	−	0.245492i	$-0.921050\pi$
$577$	−4.62979e13	+	4.62979e13i	−0.723906	+	0.723906i	0.245492	+	0.969399i	$0.421050\pi$
$578$	−2.01344e13	+	2.01344e13i	−0.312104	+	0.312104i
$579$	−2.57423e13	−	2.57423e13i	−0.395599	−	0.395599i
$580$	2.96446e11	+	2.96446e11i	0.00451654	+	0.00451654i
$581$	−1.09567e14			−1.65501
$582$		−	1.98426e13i		−	0.297156i
$583$	3.31663e13	+	3.31663e13i	0.492442	+	0.492442i
$584$		−	9.65878e13i		−	1.42186i
$585$	−3.29044e13	−	1.92245e13i	−0.480258	−	0.280592i
$586$	−5.70262e13			−0.825251
$587$	1.36427e13	−	1.36427e13i	0.195753	−	0.195753i	−0.602423	−	0.798177i	$-0.705798\pi$
$587$	1.36427e13	−	1.36427e13i	0.195753	−	0.195753i	0.798177	+	0.602423i	$0.205798\pi$
$588$	3.84876e11			0.00547563
$589$		−	1.06251e14i		−	1.49885i
$590$	−2.41976e13	+	2.41976e13i	−0.338463	+	0.338463i
$591$	−2.07092e13	+	2.07092e13i	−0.287228	+	0.287228i
$592$	3.69459e13	+	3.69459e13i	0.508110	+	0.508110i
$593$	−3.61935e13	−	3.61935e13i	−0.493580	−	0.493580i	0.415852	−	0.909432i	$-0.363483\pi$
$593$	−3.61935e13	−	3.61935e13i	−0.493580	−	0.493580i	−0.909432	+	0.415852i	$0.863483\pi$
$594$	−6.70155e13			−0.906240
$595$		−	5.24651e13i		−	0.703535i
$596$	−6.64566e11	−	6.64566e11i	−0.00883704	−	0.00883704i
$597$		−	2.93522e13i		−	0.387052i
$598$	4.23838e13	−	7.25434e13i	0.554235	−	0.948620i
$599$	2.93338e12			0.0380395			0.0190197	−	0.999819i	$-0.493945\pi$
$599$	2.93338e12			0.0380395			0.0190197	+	0.999819i	$0.493945\pi$
$600$	1.14360e13	−	1.14360e13i	0.147068	−	0.147068i
$601$	−1.20362e14			−1.53504			−0.767518	−	0.641027i	$-0.778509\pi$
$601$	−1.20362e14			−1.53504			−0.767518	+	0.641027i	$0.778509\pi$
$602$			5.18868e13i			0.656258i
$603$	3.29387e13	−	3.29387e13i	0.413161	−	0.413161i
$604$	1.41968e12	−	1.41968e12i	0.0176606	−	0.0176606i
$605$	−3.18677e13	−	3.18677e13i	−0.393164	−	0.393164i
$606$	1.57070e13	+	1.57070e13i	0.192189	+	0.192189i
$607$	−1.12356e14			−1.36350			−0.681749	−	0.731586i	$-0.738780\pi$
$607$	−1.12356e14			−1.36350			−0.681749	+	0.731586i	$0.738780\pi$
$608$		−	3.21399e12i		−	0.0386835i
$609$	2.36173e13	+	2.36173e13i	0.281931	+	0.281931i
$610$			4.84330e13i			0.573445i
$611$	6.64775e13	−	1.13782e14i	0.780672	−	1.33619i
$612$	−7.39651e11			−0.00861528
$613$	−6.32538e13	+	6.32538e13i	−0.730776	+	0.730776i	−0.970773	−	0.239998i	$-0.922853\pi$
$613$	−6.32538e13	+	6.32538e13i	−0.730776	+	0.730776i	0.239998	+	0.970773i	$0.422853\pi$
$614$	1.18184e14			1.35431
$615$		−	1.85563e13i		−	0.210919i
$616$	−1.26431e14	+	1.26431e14i	−1.42544	+	1.42544i
$617$	9.83297e13	−	9.83297e13i	1.09966	−	1.09966i	0.105211	−	0.994450i	$-0.466448\pi$
$617$	9.83297e13	−	9.83297e13i	1.09966	−	1.09966i	0.994450	−	0.105211i	$-0.0335517\pi$
$618$	2.35828e13	+	2.35828e13i	0.261609	+	0.261609i
$619$	6.20908e13	+	6.20908e13i	0.683241	+	0.683241i	0.960729	−	0.277488i	$-0.0895019\pi$
$619$	6.20908e13	+	6.20908e13i	0.683241	+	0.683241i	−0.277488	+	0.960729i	$0.589502\pi$
$620$	−7.72531e11			−0.00843252
$621$			6.62459e13i			0.717301i
$622$	−7.02420e13	−	7.02420e13i	−0.754475	−	0.754475i
$623$			1.80941e12i			0.0192795i
$624$	−8.51396e12	−	3.24435e13i	−0.0899930	−	0.342930i
$625$	4.19170e12			0.0439531
$626$	−7.92071e13	+	7.92071e13i	−0.823934	+	0.823934i
$627$	6.86026e13			0.707951
$628$			1.28749e12i			0.0131809i
$629$	−3.70083e13	+	3.70083e13i	−0.375877	+	0.375877i
$630$	−5.81934e13	+	5.81934e13i	−0.586369	+	0.586369i
$631$	9.70445e13	+	9.70445e13i	0.970117	+	0.970117i	0.999566	−	0.0294494i	$-0.00937538\pi$
$631$	9.70445e13	+	9.70445e13i	0.970117	+	0.970117i	−0.0294494	+	0.999566i	$0.509375\pi$
$632$	−8.21314e13	−	8.21314e13i	−0.814562	−	0.814562i
$633$	−4.05853e12			−0.0399347
$634$			1.25925e14i			1.22932i
$635$	9.61654e12	+	9.61654e12i	0.0931430	+	0.0931430i
$636$			2.42577e11i			0.00233112i
$637$	1.21122e14	−	3.17853e13i	1.15485	−	0.303060i
$638$	1.12109e14			1.06056
$639$	8.21050e13	−	8.21050e13i	0.770664	−	0.770664i
$640$	6.93688e13			0.646047
$641$		−	6.69530e13i		−	0.618700i	−0.950948	−	0.309350i	$-0.899889\pi$
$641$		−	6.69530e13i		−	0.618700i	0.950948	−	0.309350i	$-0.100111\pi$
$642$	−9.60527e12	+	9.60527e12i	−0.0880713	+	0.0880713i
$643$	7.88402e13	−	7.88402e13i	0.717287	−	0.717287i	−0.250762	−	0.968049i	$-0.580681\pi$
$643$	7.88402e13	−	7.88402e13i	0.717287	−	0.717287i	0.968049	+	0.250762i	$0.0806812\pi$
$644$	−1.65930e12	−	1.65930e12i	−0.0149794	−	0.0149794i
$645$	7.70920e12	+	7.70920e12i	0.0690574	+	0.0690574i
$646$	1.25263e14			1.11342
$647$			8.33185e13i			0.734886i	0.930046	+	0.367443i	$0.119767\pi$
$647$			8.33185e13i			0.734886i	−0.930046	+	0.367443i	$0.880233\pi$
$648$	−5.19617e13	−	5.19617e13i	−0.454787	−	0.454787i
$649$			1.18351e14i			1.02789i
$650$	−3.52429e13	+	6.03212e13i	−0.303742	+	0.519880i
$651$	−6.15459e13			−0.526373
$652$	9.20403e11	−	9.20403e11i	0.00781160	−	0.00781160i
$653$	1.60464e14			1.35149			0.675744	−	0.737136i	$-0.263822\pi$
$653$	1.60464e14			1.35149			0.675744	+	0.737136i	$0.263822\pi$
$654$			5.41830e13i			0.452870i
$655$	−4.83859e12	+	4.83859e12i	−0.0401340	+	0.0401340i
$656$	−8.27198e13	+	8.27198e13i	−0.680911	+	0.680911i
$657$	−1.08721e14	−	1.08721e14i	−0.888150	−	0.888150i
$658$	−2.01230e14	−	2.01230e14i	−1.63141	−	1.63141i
$659$	−2.41868e14			−1.94603			−0.973017	−	0.230732i	$-0.925888\pi$
$659$	−2.41868e14			−1.94603			−0.973017	+	0.230732i	$0.925888\pi$
$660$		−	4.98796e11i		−	0.00398293i
$661$	1.57872e13	+	1.57872e13i	0.125111	+	0.125111i	0.766890	−	0.641779i	$-0.221803\pi$
$661$	1.57872e13	+	1.57872e13i	0.125111	+	0.125111i	−0.641779	+	0.766890i	$0.721803\pi$
$662$			1.34947e14i			1.06139i
$663$	3.24983e13	−	8.52834e12i	0.253684	−	0.0665728i
$664$	1.43260e14			1.10990
$665$	1.27460e14	−	1.27460e14i	0.980092	−	0.980092i
$666$	8.20979e13			0.626558
$667$		−	1.10821e14i		−	0.839449i
$668$	−2.76036e11	+	2.76036e11i	−0.00207531	+	0.00207531i
$669$	1.71123e13	−	1.71123e13i	0.127696	−	0.127696i
$670$	4.05586e13	+	4.05586e13i	0.300406	+	0.300406i
$671$	1.18443e14	+	1.18443e14i	0.870759	+	0.870759i
$672$	−1.86170e12			−0.0135851
$673$		−	1.71760e14i		−	1.24407i	−0.782988	−	0.622036i	$-0.786306\pi$
$673$		−	1.71760e14i		−	1.24407i	0.782988	−	0.622036i	$-0.213694\pi$
$674$	−1.09252e14	−	1.09252e14i	−0.785467	−	0.785467i
$675$		−	5.50847e13i		−	0.393108i
$676$	9.08246e11	+	1.61132e12i	0.00643384	+	0.0114143i
$677$	3.92577e13			0.276046			0.138023	−	0.990429i	$-0.455925\pi$
$677$	3.92577e13			0.276046			0.138023	+	0.990429i	$0.455925\pi$
$678$	1.18518e13	−	1.18518e13i	0.0827249	−	0.0827249i
$679$	−1.80315e14			−1.24935
$680$			6.85986e13i			0.471814i
$681$	−1.86374e13	+	1.86374e13i	−0.127248	+	0.127248i
$682$	−1.46076e14	+	1.46076e14i	−0.990050	+	0.990050i
$683$	8.39338e12	+	8.39338e12i	0.0564720	+	0.0564720i	0.734779	−	0.678307i	$-0.237286\pi$
$683$	8.39338e12	+	8.39338e12i	0.0564720	+	0.0564720i	−0.678307	+	0.734779i	$0.737286\pi$
$684$	−1.79693e12	−	1.79693e12i	−0.0120019	−	0.0120019i
$685$	4.71309e13			0.312502
$686$		−	4.39295e13i		−	0.289158i
$687$	2.33337e13	+	2.33337e13i	0.152475	+	0.152475i
$688$		−	6.87316e13i		−	0.445876i
$689$	2.00334e13	+	7.63400e13i	0.129021	+	0.491650i
$690$	−3.81241e13			−0.243756
$691$	−1.41709e14	+	1.41709e14i	−0.899513	+	0.899513i	−0.995393	−	0.0958802i	$-0.969433\pi$
$691$	−1.41709e14	+	1.41709e14i	−0.899513	+	0.899513i	0.0958802	+	0.995393i	$0.469433\pi$
$692$	2.06577e12			0.0130182
$693$			2.84625e14i			1.78077i
$694$	4.88150e13	−	4.88150e13i	0.303219	−	0.303219i
$695$	−5.19598e13	+	5.19598e13i	−0.320437	+	0.320437i
$696$	−3.08798e13	−	3.08798e13i	−0.189072	−	0.189072i
$697$	−8.28595e13	−	8.28595e13i	−0.503707	−	0.503707i
$698$	9.28782e13			0.560579
$699$		−	4.82355e13i		−	0.289055i
$700$	1.37974e12	+	1.37974e12i	0.00820930	+	0.00820930i
$701$			1.08794e14i			0.642712i	0.946958	+	0.321356i	$0.104139\pi$
$701$			1.08794e14i			0.642712i	−0.946958	+	0.321356i	$0.895861\pi$
$702$	−9.73655e13	−	5.68862e13i	−0.571110	−	0.333673i
$703$	−1.79818e14			−1.04726
$704$	1.65281e14	−	1.65281e14i	0.955782	−	0.955782i
$705$	−5.97964e13			−0.343344
$706$		−	2.02029e14i		−	1.15183i
$707$	1.42734e14	−	1.42734e14i	0.808033	−	0.808033i
$708$	−4.32807e11	+	4.32807e11i	−0.00243292	+	0.00243292i
$709$	−7.40251e13	−	7.40251e13i	−0.413188	−	0.413188i	0.469659	−	0.882848i	$-0.344377\pi$
$709$	−7.40251e13	−	7.40251e13i	−0.413188	−	0.413188i	−0.882848	+	0.469659i	$0.844377\pi$
$710$	1.01099e14	+	1.01099e14i	0.560343	+	0.560343i
$711$	−1.84897e14			−1.01761
$712$		−	2.36582e12i		−	0.0129295i
$713$	1.44399e14	+	1.44399e14i	0.783638	+	0.783638i
$714$		−	7.25582e13i		−	0.391017i
$715$	−4.11935e13	−	1.56973e14i	−0.220444	−	0.840029i
$716$	3.18930e11			0.00169485
$717$	−6.60727e13	+	6.60727e13i	−0.348679	+	0.348679i
$718$	−1.38464e14			−0.725630
$719$			7.45476e13i			0.387962i	0.981005	+	0.193981i	$0.0621400\pi$
$719$			7.45476e13i			0.387962i	−0.981005	+	0.193981i	$0.937860\pi$
$720$	7.70856e13	−	7.70856e13i	0.398392	−	0.398392i
$721$	2.14304e14	−	2.14304e14i	1.09990	−	1.09990i
$722$	1.64680e14	+	1.64680e14i	0.839375	+	0.839375i
$723$	−3.93290e13	−	3.93290e13i	−0.199077	−	0.199077i
$724$	−1.54179e12			−0.00775057
$725$			9.21499e13i			0.460050i
$726$	−4.40724e13	−	4.40724e13i	−0.218516	−	0.218516i
$727$			9.65220e13i			0.475285i	0.971353	+	0.237643i	$0.0763747\pi$
$727$			9.65220e13i			0.475285i	−0.971353	+	0.237643i	$0.923625\pi$
$728$	−2.91010e14	+	7.63679e13i	−1.42315	+	0.373469i
$729$	−6.96204e13			−0.338142
$730$	1.33872e14	−	1.33872e14i	0.645766	−	0.645766i
$731$	6.88477e13			0.329839
$732$			8.66290e11i			0.00412200i
$733$	−1.65675e14	+	1.65675e14i	−0.782956	+	0.782956i	−0.980329	−	0.197373i	$-0.936759\pi$
$733$	−1.65675e14	+	1.65675e14i	−0.782956	+	0.782956i	0.197373	+	0.980329i	$0.436759\pi$
$734$	2.00754e14	−	2.00754e14i	0.942288	−	0.942288i
$735$	−4.01791e13	−	4.01791e13i	−0.187311	−	0.187311i
$736$	4.36790e12	+	4.36790e12i	0.0202248	+	0.0202248i
$737$	1.98373e14			0.912315
$738$			1.83813e14i			0.839642i
$739$	6.75182e13	+	6.75182e13i	0.306336	+	0.306336i	0.843487	−	0.537150i	$-0.180499\pi$
$739$	6.75182e13	+	6.75182e13i	0.306336	+	0.306336i	−0.537150	+	0.843487i	$0.680499\pi$
$740$			1.30742e12i			0.00589192i
$741$	9.96714e13	+	5.82334e13i	0.446149	+	0.260664i
$742$	1.70442e14			0.757806
$743$	−1.35475e14	+	1.35475e14i	−0.598293	+	0.598293i	−0.939858	−	0.341565i	$-0.889043\pi$
$743$	−1.35475e14	+	1.35475e14i	−0.598293	+	0.598293i	0.341565	+	0.939858i	$0.389043\pi$
$744$	8.04718e13			0.353004
$745$			1.38755e14i			0.604597i
$746$	1.02784e14	−	1.02784e14i	0.444867	−	0.444867i
$747$	1.61256e14	−	1.61256e14i	0.693287	−	0.693287i
$748$	−2.22727e12	−	2.22727e12i	−0.00951185	−	0.00951185i
$749$	8.72858e13	+	8.72858e13i	0.370284	+	0.370284i
$750$	8.46946e13			0.356902
$751$		−	1.85323e14i		−	0.775762i	−0.921709	−	0.387881i	$-0.873207\pi$
$751$		−	1.85323e14i		−	0.775762i	0.921709	−	0.387881i	$-0.126793\pi$
$752$	2.66559e14	+	2.66559e14i	1.10842	+	1.10842i
$753$			3.32471e13i			0.137334i
$754$	1.62881e14	+	9.51636e13i	0.668363	+	0.390494i
$755$	−2.96414e14			−1.20827
$756$	−2.22706e12	+	2.22706e12i	−0.00901826	+	0.00901826i
$757$	−3.46304e14			−1.39309			−0.696543	−	0.717515i	$-0.745280\pi$
$757$	−3.46304e14			−1.39309			−0.696543	+	0.717515i	$0.745280\pi$
$758$			5.18826e12i			0.0207336i
$759$	−9.32330e13	+	9.32330e13i	−0.370136	+	0.370136i
$760$	−1.66656e14	+	1.66656e14i	−0.657282	+	0.657282i
$761$	−5.80144e13	−	5.80144e13i	−0.227307	−	0.227307i	0.584260	−	0.811567i	$-0.301385\pi$
$761$	−5.80144e13	−	5.80144e13i	−0.227307	−	0.227307i	−0.811567	+	0.584260i	$0.801385\pi$
$762$	1.32995e13	+	1.32995e13i	0.0517678	+	0.0517678i
$763$	4.92376e14			1.90403
$764$		−	4.14695e12i		−	0.0159317i
$765$	7.72158e13	+	7.72158e13i	0.294713	+	0.294713i
$766$		−	3.81194e14i		−	1.44545i
$767$	−1.00462e14	+	1.71950e14i	−0.378465	+	0.647775i
$768$	3.67536e12			0.0137561
$769$	−1.55011e14	+	1.55011e14i	−0.576411	+	0.576411i	−0.933913	−	0.357502i	$-0.883629\pi$
$769$	−1.55011e14	+	1.55011e14i	−0.576411	+	0.576411i	0.357502	+	0.933913i	$0.383629\pi$
$770$	−3.50469e14			−1.29478
$771$			4.61979e13i			0.169570i
$772$	−4.06082e12	+	4.06082e12i	−0.0148091	+	0.0148091i
$773$	−8.81316e13	+	8.81316e13i	−0.319326	+	0.319326i	−0.848508	−	0.529182i	$-0.822499\pi$
$773$	−8.81316e13	+	8.81316e13i	−0.319326	+	0.319326i	0.529182	+	0.848508i	$0.322499\pi$
$774$	−7.63647e13	−	7.63647e13i	−0.274908	−	0.274908i
$775$	−1.20070e14	−	1.20070e14i	−0.429463	−	0.429463i
$776$	2.35764e14			0.837855
$777$			1.04159e14i			0.367784i
$778$	−2.40086e14	−	2.40086e14i	−0.842304	−	0.842304i
$779$		−	4.02603e14i		−	1.40343i
$780$	4.23403e11	−	7.24690e11i	0.00146650	−	0.00251003i
$781$	4.94476e14			1.70173
$782$	−1.70236e14	+	1.70236e14i	−0.582125	+	0.582125i
$783$	−1.48741e14			−0.505384
$784$			3.58218e14i			1.20939i
$785$	1.34407e14	−	1.34407e14i	0.450894	−	0.450894i
$786$	−6.69167e12	+	6.69167e12i	−0.0223060	+	0.0223060i
$787$	−1.21640e14	−	1.21640e14i	−0.402905	−	0.402905i	0.476351	−	0.879255i	$-0.341959\pi$
$787$	−1.21640e14	−	1.21640e14i	−0.402905	−	0.402905i	−0.879255	+	0.476351i	$0.841959\pi$
$788$	3.26686e12	+	3.26686e12i	0.0107523	+	0.0107523i
$789$	1.52988e14			0.500349
$790$		−	2.27670e14i		−	0.739897i
$791$	−1.07701e14	−	1.07701e14i	−0.347805	−	0.347805i
$792$		−	3.72150e14i		−	1.19424i
$793$	7.15433e13	+	2.72625e14i	0.228141	+	0.869359i
$794$	−5.38910e14			−1.70771
$795$	2.53238e13	−	2.53238e13i	0.0797432	−	0.0797432i
$796$	−4.63028e12			−0.0144891
$797$		−	4.70200e14i		−	1.46215i	−0.682299	−	0.731074i	$-0.739020\pi$
$797$		−	4.70200e14i		−	1.46215i	0.682299	−	0.731074i	$-0.260980\pi$
$798$	1.76275e14	−	1.76275e14i	0.544724	−	0.544724i
$799$	−2.67009e14	+	2.67009e14i	−0.819958	+	0.819958i
$800$	−3.63199e12	−	3.63199e12i	−0.0110840	−	0.0110840i
$801$	−2.66301e12	−	2.66301e12i	−0.00807625	−	0.00807625i
$802$	−3.25749e14			−0.981773
$803$		−	6.54770e14i		−	1.96115i
$804$	7.25445e11	+	7.25445e11i	0.00215936	+	0.00215936i
$805$			3.46445e14i			1.02484i
$806$	−3.36228e14	+	8.82342e13i	−0.988458	+	0.259395i
$807$	−1.28654e14			−0.375886
$808$	−1.86625e14	+	1.86625e14i	−0.541894	+	0.541894i
$809$	3.46375e14			0.999550			0.499775	−	0.866155i	$-0.333416\pi$
$809$	3.46375e14			0.999550			0.499775	+	0.866155i	$0.333416\pi$
$810$		−	1.44039e14i		−	0.413100i
$811$	3.61473e14	−	3.61473e14i	1.03032	−	1.03032i	0.0307933	−	0.999526i	$-0.490197\pi$
$811$	3.61473e14	−	3.61473e14i	1.03032	−	1.03032i	0.999526	−	0.0307933i	$-0.00980337\pi$
$812$	3.72560e12	−	3.72560e12i	0.0105540	−	0.0105540i
$813$	−2.38586e13	−	2.38586e13i	−0.0671727	−	0.0671727i
$814$	2.47217e14	+	2.47217e14i	0.691762	+	0.691762i
$815$	−1.92171e14			−0.534440
$816$			9.61137e13i			0.265665i
$817$	1.67261e14	+	1.67261e14i	0.459498	+	0.459498i
$818$		−	2.64771e13i		−	0.0722943i
$819$	−2.41605e14	+	4.13527e14i	−0.655670	+	1.12224i
$820$	−2.92724e12			−0.00789568
$821$	3.58163e14	−	3.58163e14i	0.960208	−	0.960208i	−0.0390300	−	0.999238i	$-0.512427\pi$
$821$	3.58163e14	−	3.58163e14i	0.960208	−	0.960208i	0.999238	+	0.0390300i	$0.0124268\pi$
$822$	6.51811e13			0.173685
$823$			1.61516e14i			0.427775i	0.976858	+	0.213888i	$0.0686126\pi$
$823$			1.61516e14i			0.427775i	−0.976858	+	0.213888i	$0.931387\pi$
$824$	−2.80204e14	+	2.80204e14i	−0.737629	+	0.737629i
$825$	7.75249e13	−	7.75249e13i	0.202848	−	0.202848i
$826$	3.04104e14	+	3.04104e14i	0.790899	+	0.790899i
$827$	3.54823e14	+	3.54823e14i	0.917244	+	0.917244i	0.996828	−	0.0795845i	$-0.0253593\pi$
$827$	3.54823e14	+	3.54823e14i	0.917244	+	0.917244i	−0.0795845	+	0.996828i	$0.525359\pi$
$828$	4.88416e12			0.0125499
$829$		−	4.25176e14i		−	1.08592i	−0.839760	−	0.542958i	$-0.817304\pi$
$829$		−	4.25176e14i		−	1.08592i	0.839760	−	0.542958i	$-0.182696\pi$
$830$	1.98560e14	+	1.98560e14i	0.504083	+	0.504083i
$831$			1.66781e14i			0.420863i
$832$	3.80432e14	−	9.98344e13i	0.954246	−	0.250417i
$833$	−3.58823e14			−0.894654
$834$	−7.18593e13	+	7.18593e13i	−0.178095	+	0.178095i
$835$	5.76335e13			0.141985
$836$		−	1.08220e13i		−	0.0265018i
$837$	1.93807e14	−	1.93807e14i	0.471784	−	0.471784i
$838$	−3.41500e14	+	3.41500e14i	−0.826364	+	0.826364i
$839$	−2.80208e13	−	2.80208e13i	−0.0674016	−	0.0674016i	0.672602	−	0.740004i	$-0.265176\pi$
$839$	−2.80208e13	−	2.80208e13i	−0.0674016	−	0.0674016i	−0.740004	+	0.672602i	$0.765176\pi$
$840$	9.65350e13	+	9.65350e13i	0.230828	+	0.230828i
$841$	−1.71882e14			−0.408555
$842$			4.53786e14i			1.07224i
$843$	−1.81179e14	−	1.81179e14i	−0.425569	−	0.425569i
$844$			6.40229e11i			0.00149494i
$845$	7.33974e13	−	2.63030e14i	0.170372	−	0.610550i
$846$	5.92324e14			1.36681
$847$	−4.00498e14	+	4.00498e14i	−0.918721	+	0.918721i
$848$	−2.25776e14			−0.514870
$849$			1.47965e13i			0.0335443i
$850$	1.41554e14	−	1.41554e14i	0.319027	−	0.319027i
$851$	2.44378e14	−	2.44378e14i	0.547538	−	0.547538i
$852$	1.80829e12	+	1.80829e12i	0.00402782	+	0.00402782i
$853$	4.26582e14	+	4.26582e14i	0.944620	+	0.944620i	0.998545	−	0.0539254i	$-0.0171733\pi$
$853$	4.26582e14	+	4.26582e14i	0.944620	+	0.944620i	−0.0539254	+	0.998545i	$0.517173\pi$
$854$	6.08682e14			1.33999
$855$			3.75181e14i			0.821126i
$856$	−1.14127e14	−	1.14127e14i	−0.248324	−	0.248324i
$857$		−	1.92536e12i		−	0.00416492i	−0.999998	−	0.00208246i	$-0.999337\pi$
$857$		−	1.92536e12i		−	0.00416492i	0.999998	−	0.00208246i	$-0.000662868\pi$
$858$	−5.69697e13	−	2.17090e14i	−0.122520	−	0.466879i
$859$	7.11822e14			1.52197			0.760984	−	0.648770i	$-0.224716\pi$
$859$	7.11822e14			1.52197			0.760984	+	0.648770i	$0.224716\pi$
$860$	1.21612e12	−	1.21612e12i	0.00258514	−	0.00258514i
$861$	−2.33207e14			−0.492863
$862$		−	3.89258e14i		−	0.817902i
$863$	−9.96742e13	+	9.96742e13i	−0.208223	+	0.208223i	−0.803512	−	0.595289i	$-0.797038\pi$
$863$	−9.96742e13	+	9.96742e13i	−0.208223	+	0.208223i	0.595289	+	0.803512i	$0.297038\pi$
$864$	5.86246e12	−	5.86246e12i	0.0121762	−	0.0121762i
$865$	−2.15656e14	−	2.15656e14i	−0.445329	−	0.445329i
$866$	6.91440e13	+	6.91440e13i	0.141960	+	0.141960i
$867$	7.51917e13			0.153488
$868$			9.70880e12i			0.0197046i
$869$	−5.56771e14	−	5.56771e14i	−1.12351	−	1.12351i
$870$		−	8.55995e13i		−	0.171741i
$871$	2.88212e14	+	1.68389e14i	0.574938	+	0.335910i
$872$	−6.43786e14			−1.27691
$873$	2.65380e14	−	2.65380e14i	0.523356	−	0.523356i
$874$	−8.27151e14			−1.62191
$875$		−	7.69643e14i		−	1.50055i
$876$	2.39448e12	−	2.39448e12i	0.00464185	−	0.00464185i
$877$	−3.84799e14	+	3.84799e14i	−0.741713	+	0.741713i	−0.972907	−	0.231195i	$-0.925737\pi$
$877$	−3.84799e14	+	3.84799e14i	−0.741713	+	0.741713i	0.231195	+	0.972907i	$0.425737\pi$
$878$	−1.70941e14	−	1.70941e14i	−0.327622	−	0.327622i
$879$	1.06482e14	+	1.06482e14i	0.202923	+	0.202923i
$880$	4.64247e14			0.879703
$881$			5.04078e14i			0.949769i	0.880048	+	0.474884i	$0.157510\pi$
$881$			5.04078e14i			0.949769i	−0.880048	+	0.474884i	$0.842490\pi$
$882$	3.98000e14	+	3.98000e14i	0.745660	+	0.745660i
$883$		−	2.75493e14i		−	0.513225i	−0.966514	−	0.256613i	$-0.917394\pi$
$883$		−	2.75493e14i		−	0.513225i	0.966514	−	0.256613i	$-0.0826064\pi$
$884$	−1.34534e12	−	5.12658e12i	−0.00249212	−	0.00949655i
$885$	9.03656e13			0.166451
$886$	7.52726e13	−	7.52726e13i	0.137870	−	0.137870i
$887$	−1.95611e14			−0.356266			−0.178133	−	0.984006i	$-0.557006\pi$
$887$	−1.95611e14			−0.356266			−0.178133	+	0.984006i	$0.557006\pi$
$888$		−	1.36189e14i		−	0.246648i
$889$	1.20856e14	−	1.20856e14i	0.217651	−	0.217651i
$890$	3.27906e12	−	3.27906e12i	0.00587217	−	0.00587217i
$891$	−3.52249e14	−	3.52249e14i	−0.627280	−	0.627280i
$892$	−2.69945e12	−	2.69945e12i	−0.00478025	−	0.00478025i
$893$	−1.29736e15			−2.28456
$894$			1.91895e14i			0.336028i
$895$	−3.32947e13	−	3.32947e13i	−0.0579776	−	0.0579776i
$896$		−	8.71794e14i		−	1.50964i
$897$	−2.14597e14	+	5.63155e13i	−0.369541	+	0.0969763i
$898$	7.61610e14			1.30422
$899$	−3.24216e14	+	3.24216e14i	−0.552123	+	0.552123i
$900$	−4.06127e12			−0.00687780
$901$		−	2.26157e14i		−	0.380878i
$902$	−5.53506e14	+	5.53506e14i	−0.927020	+	0.927020i
$903$	9.68855e13	−	9.68855e13i	0.161369	−	0.161369i
$904$	1.40820e14	+	1.40820e14i	0.233250	+	0.233250i
$905$	1.60955e14	+	1.60955e14i	0.265132	+	0.265132i
$906$	−4.09934e14			−0.671542
$907$			1.08507e14i			0.176775i	0.996086	+	0.0883877i	$0.0281714\pi$
$907$			1.08507e14i			0.176775i	−0.996086	+	0.0883877i	$0.971829\pi$
$908$	2.94003e12	+	2.94003e12i	0.00476346	+	0.00476346i
$909$			4.20138e14i			0.676974i
$910$	−5.09190e14	−	2.97496e14i	−0.815968	−	0.476732i
$911$	4.70154e14			0.749287			0.374644	−	0.927169i	$-0.377765\pi$
$911$	4.70154e14			0.749287			0.374644	+	0.927169i	$0.377765\pi$
$912$	−2.33502e14	+	2.33502e14i	−0.370097	+	0.370097i
$913$	9.71163e14			1.53087
$914$		−	5.91211e13i		−	0.0926855i
$915$	9.04362e13	−	9.04362e13i	0.141006	−	0.141006i
$916$	3.68087e12	−	3.68087e12i	0.00570785	−	0.00570785i
$917$	6.08091e13	+	6.08091e13i	0.0937825	+	0.0937825i
$918$	2.28485e14	+	2.28485e14i	0.350465	+	0.350465i
$919$	4.21691e13			0.0643305			0.0321652	−	0.999483i	$-0.489760\pi$
$919$	4.21691e13			0.0643305			0.0321652	+	0.999483i	$0.489760\pi$
$920$		−	4.52980e14i		−	0.687289i
$921$	−2.20679e14	−	2.20679e14i	−0.333015	−	0.333015i
$922$		−	4.31290e13i		−	0.0647313i
$923$	7.18415e14	+	4.19737e14i	1.07242	+	0.626568i
$924$	−6.26863e12			−0.00930706
$925$	−2.03205e14	+	2.03205e14i	−0.300072	+	0.300072i
$926$	1.58767e14			0.233188
$927$			6.30805e14i			0.921502i
$928$	−9.80718e12	+	9.80718e12i	−0.0142497	+	0.0142497i
$929$	−4.91000e14	+	4.91000e14i	−0.709583	+	0.709583i	−0.966447	−	0.256865i	$-0.917311\pi$
$929$	−4.91000e14	+	4.91000e14i	−0.709583	+	0.709583i	0.256865	+	0.966447i	$0.417311\pi$
$930$	1.11535e14	+	1.11535e14i	0.160323	+	0.160323i
$931$	−8.71735e14	−	8.71735e14i	−1.24634	−	1.24634i
$932$	−7.60910e12			−0.0108207
$933$			2.62318e14i			0.371040i
$934$	1.79686e14	+	1.79686e14i	0.252802	+	0.252802i
$935$			4.65031e14i			0.650765i
$936$	3.15900e14	−	5.40690e14i	0.439714	−	0.752608i
$937$	−9.70318e14			−1.34343			−0.671717	−	0.740808i	$-0.734443\pi$
$937$	−9.70318e14			−1.34343			−0.671717	+	0.740808i	$0.734443\pi$
$938$	5.09721e14	−	5.09721e14i	0.701969	−	0.701969i
$939$	2.95798e14			0.405198
$940$			9.43283e12i			0.0128529i
$941$	2.01191e14	−	2.01191e14i	0.272685	−	0.272685i	−0.557495	−	0.830180i	$-0.688237\pi$
$941$	2.01191e14	−	2.01191e14i	0.272685	−	0.272685i	0.830180	+	0.557495i	$0.188237\pi$
$942$	1.85883e14	−	1.85883e14i	0.250602	−	0.250602i
$943$	5.47149e14	+	5.47149e14i	0.733749	+	0.733749i
$944$	−4.02829e14	−	4.02829e14i	−0.537354	−	0.537354i
$945$	4.64987e14			0.616996
$946$		−	4.59906e14i		−	0.607034i
$947$	4.71899e13	+	4.71899e13i	0.0619582	+	0.0619582i	0.737407	−	0.675449i	$-0.236050\pi$
$947$	4.71899e13	+	4.71899e13i	0.0619582	+	0.0619582i	−0.675449	+	0.737407i	$0.736050\pi$
$948$		−	4.07220e12i		−	0.00531847i
$949$	5.55802e14	−	9.51303e14i	0.722087	−	1.23591i
$950$	6.87791e14			0.888870
$951$	2.35133e14	−	2.35133e14i	0.302281	−	0.302281i
$952$	8.62115e14			1.10250
$953$			6.37542e14i			0.811043i	0.914085	+	0.405522i	$0.132910\pi$
$953$			6.37542e14i			0.811043i	−0.914085	+	0.405522i	$0.867090\pi$
$954$	−2.50849e14	+	2.50849e14i	−0.317447	+	0.317447i
$955$	−4.32920e14	+	4.32920e14i	−0.544993	+	0.544993i
$956$	1.04229e13	+	1.04229e13i	0.0130527	+	0.0130527i
$957$	−2.09335e14	−	2.09335e14i	−0.260784	−	0.260784i
$958$	−1.42773e15			−1.76937
$959$		−	5.92319e14i		−	0.730234i
$960$	−1.26198e14	−	1.26198e14i	−0.154774	−	0.154774i
$961$		−	2.52685e13i		−	0.0308292i
$962$	1.49326e14	+	5.69027e14i	0.181243	+	0.690649i
$963$	−2.56927e14			−0.310226
$964$	−6.20411e12	+	6.20411e12i	−0.00745236	+	0.00745236i
$965$	8.47858e14			1.01318
$966$			4.79126e14i			0.569592i
$967$	−4.89842e14	+	4.89842e14i	−0.579327	+	0.579327i	−0.934718	−	0.355391i	$-0.884348\pi$
$967$	−4.89842e14	+	4.89842e14i	−0.579327	+	0.579327i	0.355391	+	0.934718i	$0.384348\pi$
$968$	5.23655e14	−	5.23655e14i	0.616125	−	0.616125i
$969$	−2.33896e14	−	2.33896e14i	−0.273781	−	0.273781i
$970$	3.26772e14	+	3.26772e14i	0.380528	+	0.380528i
$971$	1.02550e15			1.18806			0.594031	−	0.804442i	$-0.297535\pi$
$971$	1.02550e15			1.18806			0.594031	+	0.804442i	$0.297535\pi$
$972$		−	1.00469e13i		−	0.0115798i
$973$	6.53006e14	+	6.53006e14i	0.748777	+	0.748777i
$974$			1.12562e15i			1.28409i
$975$	1.78442e14	−	4.68273e13i	0.202522	−	0.0531467i
$976$	−8.06288e14			−0.910418
$977$	8.93601e13	−	8.93601e13i	0.100385	−	0.100385i	−0.655130	−	0.755516i	$-0.727386\pi$
$977$	8.93601e13	−	8.93601e13i	0.100385	−	0.100385i	0.755516	+	0.655130i	$0.227386\pi$
$978$	−2.65768e14			−0.297036
$979$		−	1.60379e13i		−	0.0178334i
$980$	−6.33821e12	+	6.33821e12i	−0.00701190	+	0.00701190i
$981$	−7.24656e14	+	7.24656e14i	−0.797604	+	0.797604i
$982$	−4.93783e14	−	4.93783e14i	−0.540728	−	0.540728i
$983$	3.19159e14	+	3.19159e14i	0.347728	+	0.347728i	0.859263	−	0.511535i	$-0.170923\pi$
$983$	3.19159e14	+	3.19159e14i	0.347728	+	0.347728i	−0.511535	+	0.859263i	$0.670923\pi$
$984$	3.04921e14			0.330530
$985$		−	6.82087e14i		−	0.735629i
$986$	−3.82227e14	−	3.82227e14i	−0.410145	−	0.410145i
$987$			7.51493e14i			0.802305i
$988$	9.18626e12	−	1.57231e13i	0.00975784	−	0.0167014i
$989$	−4.54625e14			−0.480476
$990$	5.15805e14	−	5.15805e14i	0.542388	−	0.542388i
$991$	−6.71014e14			−0.702043			−0.351021	−	0.936367i	$-0.614166\pi$
$991$	−6.71014e14			−0.702043			−0.351021	+	0.936367i	$0.614166\pi$
$992$		−	2.55572e13i		−	0.0266045i
$993$	2.51979e14	−	2.51979e14i	0.260987	−	0.260987i
$994$	1.27056e15	−	1.27056e15i	1.30937	−	1.30937i
$995$	4.83378e14	+	4.83378e14i	0.495646	+	0.495646i
$996$	3.55152e12	+	3.55152e12i	0.00362341	+	0.00362341i
$997$	1.98789e14			0.201798			0.100899	−	0.994897i	$-0.467828\pi$
$997$	1.98789e14			0.201798			0.100899	+	0.994897i	$0.467828\pi$
$998$			1.51043e15i			1.52562i
$999$	−3.27997e14	−	3.27997e14i	−0.329642	−	0.329642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.11.d.a.5.3	✓	20
13.8	odd	4	inner	13.11.d.a.8.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.11.d.a.5.3	✓	20	1.1	even	1	trivial
13.11.d.a.8.3	yes	20	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.7752 + 22.7752i) q^{2} +85.0537 q^{3} -13.4171i q^{4} +(-1400.68 + 1400.68i) q^{5} +(-1937.11 + 1937.11i) q^{6} +(17603.1 + 17603.1i) q^{7} +(-23016.2 - 23016.2i) q^{8} -51814.9 q^{9} -63801.5i q^{10} +(-156027. - 156027. i) q^{11} -1141.18i q^{12} +(-94245.1 - 359133. i) q^{13} -801827. q^{14} +(-119133. + 119133. i) q^{15} +1.06214e6 q^{16} +1.06393e6i q^{17} +(1.18009e6 - 1.18009e6i) q^{18} +(-2.58474e6 + 2.58474e6i) q^{19} +(18793.1 + 18793.1i) q^{20} +(1.49721e6 + 1.49721e6i) q^{21} +7.10710e6 q^{22} -7.02548e6i q^{23} +(-1.95761e6 - 1.95761e6i) q^{24} +5.84181e6i q^{25} +(1.03258e7 + 6.03286e6i) q^{26} -9.42938e6 q^{27} +(236183. - 236183. i) q^{28} +1.57742e7 q^{29} -5.42655e6i q^{30} +(-2.05535e7 + 2.05535e7i) q^{31} +(-621723. + 621723. i) q^{32} +(-1.32707e7 - 1.32707e7i) q^{33} +(-2.42312e7 - 2.42312e7i) q^{34} -4.93126e7 q^{35} +695207. i q^{36} +(3.47845e7 + 3.47845e7i) q^{37} -1.17736e8i q^{38} +(-8.01589e6 - 3.05456e7i) q^{39} +6.44767e7 q^{40} +(-7.78807e7 + 7.78807e7i) q^{41} -6.81983e7 q^{42} -6.47108e7i q^{43} +(-2.09344e6 + 2.09344e6i) q^{44} +(7.25761e7 - 7.25761e7i) q^{45} +(1.60007e8 + 1.60007e8i) q^{46} +(2.50965e8 + 2.50965e8i) q^{47} +9.03385e7 q^{48} +3.37262e8i q^{49} +(-1.33048e8 - 1.33048e8i) q^{50} +9.04911e7i q^{51} +(-4.81853e6 + 1.26450e6i) q^{52} -2.12568e8 q^{53} +(2.14756e8 - 2.14756e8i) q^{54} +4.37089e8 q^{55} -8.10312e8i q^{56} +(-2.19842e8 + 2.19842e8i) q^{57} +(-3.59260e8 + 3.59260e8i) q^{58} +(-3.79263e8 - 3.79263e8i) q^{59} +(1.59842e6 + 1.59842e6i) q^{60} -7.59120e8 q^{61} -9.36221e8i q^{62} +(-9.12102e8 - 9.12102e8i) q^{63} +1.05931e9i q^{64} +(6.35038e8 + 3.71023e8i) q^{65} +6.04485e8 q^{66} +(-6.35699e8 + 6.35699e8i) q^{67} +1.42749e7 q^{68} -5.97543e8i q^{69} +(1.12310e9 - 1.12310e9i) q^{70} +(-1.58458e9 + 1.58458e9i) q^{71} +(1.19258e9 + 1.19258e9i) q^{72} +(2.09826e9 + 2.09826e9i) q^{73} -1.58445e9 q^{74} +4.96868e8i q^{75} +(3.46798e7 + 3.46798e7i) q^{76} -5.49312e9i q^{77} +(8.78244e8 + 5.13117e8i) q^{78} +3.56842e9 q^{79} +(-1.48771e9 + 1.48771e9i) q^{80} +2.25761e9 q^{81} -3.54749e9i q^{82} +(-3.11216e9 + 3.11216e9i) q^{83} +(2.00882e7 - 2.00882e7i) q^{84} +(-1.49022e9 - 1.49022e9i) q^{85} +(1.47380e9 + 1.47380e9i) q^{86} +1.34165e9 q^{87} +7.18231e9i q^{88} +(5.13947e7 + 5.13947e7i) q^{89} +3.30587e9i q^{90} +(4.66284e9 - 7.98085e9i) q^{91} -9.42618e7 q^{92} +(-1.74816e9 + 1.74816e9i) q^{93} -1.14315e10 q^{94} -7.24079e9i q^{95} +(-5.28798e7 + 5.28798e7i) q^{96} +(-5.12170e9 + 5.12170e9i) q^{97} +(-7.68120e9 - 7.68120e9i) q^{98} +(8.08453e9 + 8.08453e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) \) 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

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